Mathematics

# Evaluate the following integrals :$\displaystyle\int_{0}^{\pi} x\ dx$

##### SOLUTION

$\displaystyle\int_{0}^{\pi} x\ dx$

Using $\displaystyle\int{{x}^{n}dx}=\dfrac{{x}^{n+1}}{n+1}+c$, we get

$\Rightarrow \left[\dfrac {x^2}2\right]_0^\pi$

$\Rightarrow \dfrac {\pi^2}2$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Hard
Evaluate: $\displaystyle\int \dfrac{1-x^2}{x(1-2x)}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Solve: $\displaystyle \int \dfrac{\sin 2x}{\sin \left(x - \dfrac{\pi}{4}\right) .\sin \left(x + \dfrac{\pi}{4}\right)} dx$
• A. $\log\left |\sin^2 x + \dfrac{1}{2}\right|$
• B. $\log\left |\sin x - \dfrac{1}{2}\right|$
• C. $\log\left |\sin^2 x + \dfrac{1}{\sqrt{2}}\right|$
• D. $\log\left |\sin^2 x - \dfrac{1}{2}\right|$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate $\displaystyle\int\limits_0^\pi {\dfrac{{x\sin x}}{{1 + {{\cos }^2}x}}dx}$
• A. $\dfrac{3\pi}{4}$
• B. $\dfrac{\pi}{4}$
• C. $\dfrac{5\pi}{4}$
• D. $-\dfrac{\pi}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\int { \dfrac { { x }^{ 2 } }{ \sqrt { { x }^{ 6 }+{ a }^{ 6 } } } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
Evaluate $\displaystyle\int{\frac{dx}{\sqrt{(x-a)(b-x)}}}$.
• A. $\displaystyle I=2\cos^{-1}{\sqrt{\frac{x-a}{(b-a)}}}+C$
• B. $\displaystyle I=\sin^{-1}{\sqrt{\frac{x-a}{(b-a)}}}+C$
• C. $\displaystyle I=2\sin^{-1}{\sqrt{\frac{x-b}{(a-b)}}}+C$
• D. $\displaystyle I=2\sin^{-1}{\sqrt{\frac{x-a}{(b-a)}}}+C$