Mathematics

Single Correct Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
The value of $$\displaystyle \int_{-8}^{8} (\sin^{93} x + x^{295}) dx $$
  • A. $$1$$
  • B. $$-1$$
  • C. $$\dfrac {8}{3}$$
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Medium
By using the properties of definite integrals, evaluate the integral   $$\displaystyle \int_0^{\tfrac {\pi}{2}}\frac {\cos^5xdx}{\sin^5x+\cos^5x}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
Evaluate $$\displaystyle\int^2_1 log x dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 TRUE/FALSE Medium
If $$In\int x^n(a-x)^{1/2}dx$$ then $$I_n=\dfrac{2an}{2n+3}I_{n-1}-\dfrac{2x^n(a-x)^{3/2}}{2n+3}$$
  • A. False
  • B. True

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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