Mathematics

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


ANSWER

$$2\pi$$


View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

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. $$\displaystyle -\sqrt{1-x^{2}}\sin ^{-1}x+x.$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\displaystyle \frac{1}{32}\left ( \pi +\frac{7\sqrt{3}}{2}-8 \right )$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Integrate the function $$\frac{1}{\sqrt{(2-x)^2+1}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer