Mathematics

# The value of $\displaystyle \int_{-\pi}^{\pi}(\cos px-\sin qx)^2 dx$, where $p$ and $q$ are integers is

$2\pi$

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle\int \frac{x\sin ^{-1}x}{\sqrt{\left ( 1-x^{2} \right )}}dx.$
• A. $\displaystyle \sqrt{1-x^{2}}\sin ^{-1}x+x.$
• B. $\displaystyle -\sqrt{1-x^{2}}\cos ^{-1}x+x.$
• C. $\displaystyle -\sqrt{1-x^{2}}\sin ^{-1}x-x.$
• D. $\displaystyle -\sqrt{1-x^{2}}\sin ^{-1}x+x.$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium

$\displaystyle \int_{a}^{b}f(a+b-x)dx =\displaystyle \int_{a}^{b}f(x)dx$ is true
• A. For a $=$ 0 only
• B. For all values of a only
• C. For all values of b only
• D. For all values of a,b

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Solve $\displaystyle \int_{\sqrt{2}}^{1}\frac{dx}{x^{5}\sqrt{x^{2}-1}}$
• A. $\displaystyle \frac{1}{32}\left ( \pi -\frac{7\sqrt{3}}{2}-8 \right )$
• B. $\displaystyle \frac{1}{32}\left ( \pi +\frac{7\sqrt{3}}{2}+8 \right )$
• C. None of these
• D. $\displaystyle \frac{1}{32}\left ( \pi +\frac{7\sqrt{3}}{2}-8 \right )$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral:
$\int { \cfrac { { \left( 1+\sqrt { x } \right) }^{ 2 } }{ \sqrt { x } } } dx$

Integrate the function $\frac{1}{\sqrt{(2-x)^2+1}}$