Mathematics

# Let $f\left( x \right) =\int _{ 0 }^{ x }{ f(t)dt. }$ if ${ f\left( { x }^{ 2 } \right) }={ x }^{ 2 }(1+x),$ f(4) equals

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Multiple Correct Hard
$\displaystyle \int \displaystyle \frac{x^{2}+\cos ^{2}x}{1+x^{2}}\csc^{2}xdx$ is equal to:
• A. $\cot x-\cot ^{-1}x+c$
• B. $e^{\ln\tan^2x}+\cos x +c$
• C. $c-\cot x+\cot ^{-1}x$
• D. $- \tan^{-1}x-\displaystyle \frac{\csc x}{\sec x}+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^{\pi/2}_{\pi/3}\dfrac{\sqrt{1+\cos x}}{(1-\cos x)^{5/2}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate:
$\frac { 1 } { \sqrt { 16 - 9 x ^ { 2 } } }$

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Hard
$\displaystyle \int_{0}^{\pi /2}\log \sin x dx= \frac{\pi }{k}\log \frac{1}{2}.$ Find the value of $k$.

Evaluate $\displaystyle \int x^{2}e^{x}dx$.