Mathematics

Single Correct Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
The value of $$\displaystyle \int_2^4 \left( \dfrac{\log  t}{t} \right ) dt$$ is
  • A. $$\dfrac{1}{2} (\log 2)^2$$
  • B. $$\dfrac{5}{2} (\log 2)^2$$
  • C. $$(\log 2)^2$$
  • D. $$\dfrac{3}{2} (\log 2)$$
  • E. $$\dfrac{3}{2} (\log 2)^2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
(A) : $$\displaystyle \int e^{x}(\log x+x^{-2})dx={ e }^{ x }\left( \log  x-\frac { 1 }{ x }  \right) +c$$
(R): $$\displaystyle \int e^{x}[f(x)+f'(x)]dx=e^{x}f(x)+c$$
  • A. Both A and R are true but R is not correct explanation of A
  • B. A is true but R is false
  • C. A is false but R is true.
  • D. Both A and R are true and R is the correct explanation of A

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Hard
If $$\displaystyle \int x^{5}(1+x^{3})^{2/3}dx=A(1+x^{3})^{8/3}+B(1+x^{3})^{5/3}+c$$, then 
  • A. $$A=\dfrac{1}{8},B=-\dfrac{1}{5}$$
  • B. $$A=-\dfrac{1}{8},B=\dfrac{1}{5}$$
  • C. None of these
  • D. $$A=\dfrac{1}{4},B=\dfrac{1}{5}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Evaluate the following integrals:
$$\int { \sin ^{ 3 }{ x } \cos ^{ 5 }{ x }  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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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

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