Home
Category
Sub-Category

Tap to switch levels
- Numbers
- Measurement
- Data Analysis
- Geometry
- Ratio and Percentage
- Speed
- Algebra
- Others
- Integration

SEAMO Paper C

SEAMO Paper C Preparation

SEAMO PRACTICE TOPIC #1

SEAMO PRACTICE TOPIC #2

SEAMO PRACTICE TOPIC #3

SEAMO PRACTICE TOPIC #4

SEAMO PRACTICE TOPIC #5

SEAMO PRACTICE TOPIC #6

SEAMO PRACTICE TOPIC #7

SEAMO PRACTICE TOPIC #8

SEAMO PRACTICE TOPIC #9

SEAMO PRACTICE TOPIC #10

SEAMO PRACTICE TOPIC #11

SEAMO PRACTICE TOPIC #12

SEAMO PRACTICE TOPIC #13

SEAMO PRACTICE TOPIC #14

SEAMO PRACTICE TOPIC #15

SEAMO PRACTICE TOPIC #16

SEAMO PRACTICE TOPIC #17

SEAMO PRACTICE TOPIC #18

SEAMO PRACTICE TOPIC #19

SEAMO PRACTICE TOPIC #20

SEAMO PRACTICE TOPIC #21

SEAMO PRACTICE TOPIC #22

SEAMO PRACTICE TOPIC #23

SEAMO PRACTICE TOPIC #24

SEAMO PRACTICE TOPIC #25

A-Level Maths

Integration

A-Level Math: Definite Integrals

Integration

Question 1 of 12

Find $\int\frac{2}{(1-x)(x^2+1)}dx$

Select An Answer

$\frac{1}{2}\ln\frac{x^2+1}{(1-x)^2}+C$

$\frac{1}{3}\ln\frac{x^2+2}{(1-x)^2}+C$

$\frac{1}{2}\ln\frac{2x^2+1}{(1-x)^2}+C$

$\frac{1}{2}\ln\frac{x^2+1}{(1+x)^2}+C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$\frac{1}{2}\ln\frac{x^2+1}{(1-x)^2}+C$

Yay! Your are right.

Find $\int\frac{4x^2+2x+2}{4x^2+2x+1}dx$.

Select An Answer

$x+\frac{1}{\sqrt{3}}\tan^{-1}\frac{3x+1}{\sqrt{3}}+C$

$x+\frac{1}{\sqrt{3}}\tan^{-1}\frac{4x+1}{\sqrt{3}}+C$

$x+\frac{1}{\sqrt{2}}\tan^{-1}\frac{4x+1}{\sqrt{3}}+C$

$x+\frac{1}{\sqrt{6}}\tan^{-1}\frac{4x+1}{\sqrt{3}}+C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$x+\frac{1}{\sqrt{3}}\tan^{-1}\frac{4x+1}{\sqrt{3}}+C$

Yay! Your are right.

Find $\int\frac{16x+5}{4x^2+2x+1}dx$.

Select An Answer

$2\ln(4x^2+2x+1)+\frac{1}{\sqrt{3}}\tan^{-1}\frac{4x+1}{\sqrt{3}}$.

$3\ln(4x^2+2x+1)+\frac{1}{\sqrt{3}}\tan^{-1}\frac{2x+1}{\sqrt{3}}$.

$3\ln(4x^2+2x+1)+\frac{1}{\sqrt{3}}\tan^{-1}\frac{3x+1}{\sqrt{3}}$.

$2\ln(4x^2+2x+1)+\frac{1}{\sqrt{2}}\tan^{-1}\frac{4x+1}{\sqrt{3}}$.

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$2\ln(4x^2+2x+1)+\frac{1}{\sqrt{3}}\tan^{-1}\frac{4x+1}{\sqrt{3}}$.

Yay! Your are right.

Using the substitution of $u=1-x$, or otherwise, find $\int x^2(1-x)^7dx$.

Select An Answer

$-\frac{(1-x)^8}{8}+\frac{2(1-x)^9}{9}-\frac{(1-x)^{10}}{10}+C$

$-\frac{(1-x)^8}{8}+\frac{3(1-x)^8}{8}-\frac{(1-x)^{10}}{8}+C$

$-\frac{(1-x)^8}{8}+\frac{2(1-x)^8}{9}-\frac{(1-x)^{9}}{10}+C$

$-\frac{(1-x)^8}{8}+\frac{2(1-x)^9}{8}-\frac{(1-x)^{9}}{9}+C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$-\frac{(1-x)^8}{8}+\frac{2(1-x)^9}{9}-\frac{(1-x)^{10}}{10}+C$

Yay! Your are right.

Using the substitution $x=\sin\theta$, or otherwise, find $\int\frac{x^2}{\sqrt{1-x^2}}dx$.

Select An Answer

$\frac{\sin^{-1}x}{2}-\frac{x\sqrt{1-x^2}}{3}+C$

$\frac{\sin^{-1}x}{3}-\frac{x\sqrt{1-x^2}}{2}+C$

$\frac{\sin^{-1}x}{2}-\frac{x\sqrt{1-x^2}}{2}+C$

$\frac{\sin^{-1}x}{3}-\frac{x\sqrt{1-x^2}}{3}+C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$\frac{\sin^{-1}x}{2}-\frac{x\sqrt{1-x^2}}{2}+C$

Yay! Your are right.

Using the integration by parts, $\int udv = uv - \int vdu$, and the variation $\int uv dx = u\int vdx - \int u^{'}\left(\int v du\right) dx$, find $\int e^x tan^{-1}(e^x)dx$.

Select An Answer

$e^{x}\tan^{-1}e^{2x}-\frac{1}{4}\ln\left|e^{2x}+1\right|+C$.

$e^{x}\tan^{-1}e^{2x}-\frac{1}{2}\ln\left|e^{2x}+1\right|+C$.

$e^{x}\tan^{-1}e^{2x}-\frac{1}{2}\ln\left|e^{2x}+2\right|+C$.

$e^{x}\tan^{-2}e^{2x}-\frac{1}{4}\ln\left|e^{2x}+1\right|+C$.

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$e^{x}\tan^{-1}e^{2x}-\frac{1}{2}\ln\left|e^{2x}+1\right|+C$.

Yay! Your are right.

Sometimes, if the integrand does not contain a product of functions, we can create a product by Introducing a '1'. and we can integrate 1, that is, $v=1$. Find $\int\ln dx$.

Select An Answer

$x\ln x - x + C$

$xe^x - x + C$

$x\ln x - 2x + C$

$xe^2 - x + C$

None of the above

Sorry. Please check the correct answer below.

Sometimes, the question requires you to first differnentiate and/or integrate some functions followed by applying these results to find the integral of another function. Remember that integration is the reverse of differentiation, $\int\frac{dy}{dx}dx = y+C$. Show that $\frac{d}{dx}\tan^3x = 3sec^4x-3sec^2x$, and find $\int sec^4xdx$.

Select An Answer

$\frac{1}{3}\tan^3x+\tan x + C$

$\frac{1}{2}\tan^3x+\tan x + C$

$\frac{1}{3}\tan^2x+\tan x + C$

$\frac{1}{2}\tan^2x+\tan x + C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$\frac{1}{3}\tan^3x+\tan x + C$

Yay! Your are right.

Using $\int f^{'}(x)[f(x)]^n dx = \frac{[f(x)]^{n+1}}{n+1}+C$, find $\int \frac{x^3}{\sqrt{4-x^4}}dx$.

Select An Answer

$-\frac{1}{3}{(4-x^4})^{\frac{1}{2}}+C$

$-\frac{1}{2}{(4-x^4})^{\frac{1}{2}}+C$

$-\frac{1}{4}{(4-x^4})^{\frac{1}{2}}+C$

$-\frac{1}{6}{(4-x^4})^{\frac{1}{2}}+C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$-\frac{1}{2}{(4-x^4})^{\frac{1}{2}}+C$

Yay! Your are right.

Using $\int f^{'}a^{f(x)} dx = \frac{a^{f(x)}}{\ln a} + C$, where $a>0$, find $\int x(5^{x^2})dx$.

Select An Answer

$\frac{5^{x^2}}{2\ln5}+C$

$\frac{5^{x^2}}{2\ln6}+C$

$\frac{5^{x^2}}{4\ln5}+C$

$\frac{5^{x^2}}{3\ln5}+C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$\frac{5^{x^2}}{2\ln5}+C$

Yay! Your are right.

Using $\int f^{'}(x)[f(x)]^n dx = \frac{[f(x)]^{n+1}}{n+1}+C$, find $\int \frac{e^{-2x}}{\left(2-e^{-2x}\right)^3}dx$.

Select An Answer

$\frac{-1}{4(2-e^{-2x})^2}+C$.

$\frac{-1}{3(2-e^{-2x})^2}+C$.

$\frac{-1}{2(2-e^{-2x})^2}+C$.

$\frac{-1}{6(2-e^{-2x})^2}+C$.

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$\frac{-1}{4(2-e^{-2x})^2}+C$.

Yay! Your are right.

Using $\int f^{'}a^{f(x)} dx = \frac{a^{f(x)}}{\ln a} + C$, where $a>0$, find $\frac{1}{x}\left(2^{\ln x^3}\right)dx$.

Select An Answer

$\frac{2^{\ln x^3}}{3\ln 2}+C$

$\frac{2^{\ln x^2}}{3\ln 2}+C$

$\frac{2^{\ln x^3}}{2\ln 3}+C$

$\frac{2^{\ln x^2}}{2\ln 3}+C$

None of the above

Sorry. Please check the correct answer below.

View Correct Answer

$\frac{2^{\ln x^3}}{3\ln 2}+C$

Yay! Your are right.

Tap to switch levels

SEAMO Paper C

A-Level Maths

Integration

Question 1 of 12

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

Select An Answer

View Correct Answer

General

Contact Us

What subject area do you need help in?

Ok, Let's confirm where you'll need help.

Nice! 20 tutors are near you.

By clicking "Join now". you agree to our Terms of Use and Privacy Policy

Are you a Tutor or Tuition Center?

Tell us about yourself

By clicking "Join now". you agree to our Terms of Use and Privacy Policy

Your company's contact information

By clicking "Join now". you agree to our Terms of Use and Privacy Policy