Passage
Let $$\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$$Then answer the following question.
Mathematics
$$\int_{0}^{\pi }xf\left ( x \right )dx=$$
A
$$0$$
B
$$\displaystyle \frac{8}{\pi }$$
C
$$\displaystyle \frac{16}{\pi ^{2}}$$
D
$$\displaystyle \frac{8}{\pi ^{2}}$$
Single Correct
Medium
Published on 17th 09, 2020
Mathematics
$$\int_{0}^{\pi }f\left ( x \right )dx=$$
A
$$\displaystyle \frac{4}{\pi }$$
B
$$\displaystyle \frac{8}{\pi }$$
C
$$\displaystyle \frac{8}{\pi ^{2}}$$
D
$$0$$
Single Correct
Hard
Published on 17th 09, 2020
Questions
203550
Subjects
9
Chapters
126
Enrolled Students
334
Realted Questions
Q1
Single Correct
Medium
$$\int _{ 0 }^{ \pi }{ x } In\left( \sin { x } \right) dx=$$
- A. $$\dfrac { \pi }{ 2 } ln\ 2$$
- B. $$\dfrac { -{ \pi }^{ 2 } }{ 2 } ln\ 2$$
- C. $$-\dfrac { \pi }{ 2 } ln2$$
- D. $$\ ln\ 2$$
Asked in: Mathematics - Integrals
1 Verified Answer | Published on 17th 09, 2020
View Answer
Q2
Subjective
Medium
Evaluate $$\int \tan^{-1}\left\{\sqrt{\left(\dfrac{1-\cos 2 x}{1+ \cos2 x}\right)}\right\}dx$$
Asked in: Mathematics - Integrals
1 Verified Answer | Published on 17th 09, 2020
View Answer
Q3
Subjective
Hard
Evaluate $$\displaystyle{\int}^{\pi}_0 \dfrac{x \sin x}{1+\cos^2 x}dx$$.
Asked in: Mathematics - Integrals
1 Verified Answer | Published on 17th 09, 2020
View Answer
Q4
Single Correct
Medium
$$\displaystyle \int_{0}^{\pi/2}\frac{\cos^4x}{\cos^4x+\sin^4x}dx=?$$
- A. $$\dfrac{\pi}{4}$$
- B. $$\dfrac{\pi}{2}$$
- C. $$\dfrac{\pi}{8}$$
- D. $$\pi$$
Asked in: Mathematics - Integrals
1 Verified Answer | Published on 17th 09, 2020
View Answer
Q5
One Word
Hard
$$\displaystyle \int \frac{\cos x}{5-3\cos x}dx=-\frac{1}{3}x+\frac{k}{6}\tan ^{-1}\left [ 2\tan \frac{x}{2} \right ].$$ Find the value of $$k$$.
Asked in: Mathematics - Integrals
1 Verified Answer | Published on 17th 09, 2020
View Answer