Mathematics

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 124
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
Let $$f(x)=\displaystyle \frac{1}{3}\cot^{3}x-\cot x+\int\cot^{4}xdx$$ and $$f(\displaystyle \frac{\pi}{2})=\frac{\pi}{2}$$ , then $$f(x) =$$
  • A. $$\pi-x$$
  • B. $$ x-\pi $$
  • C. $$ \dfrac{\pi}{2}-x$$
  • D. $$ x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate:
$$\displaystyle\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sin ^5 x\ dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium

$$\int frac{2^x + 3^x}{5^x} dx equals-

  • A. (b)$$lo{g_e}(2x/5) + lo{g_e}(3x/5) + C$$
  • B. (c)$$x + C$$
  • C. None of these
  • D. (a)$$\frac{(2/5)^x}{log_e 2/5} + \frac{(3/5)^x}{log_e 3/5} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle\int { \dfrac { { x }^{ n-1 } }{ { x }^{ 2n }+{ a }^{ 2 } } dx } $$ is equal to
  • A. $$\dfrac { 1 }{ na } \tan ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$$
  • B. $$\dfrac { n }{ a } \sin ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$$
  • C. $$\dfrac { n }{ a } \cos ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$$
  • D. $$\dfrac { 1 }{ na } \cot ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$$
  • E. $$\dfrac { n }{ a } \tan ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

View Answer