Mathematics

Single Correct Medium Published on 17th 09, 2020
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Realted Questions

Q1 Subjective Medium
Evaluate the following integrals:
$$\int { \cfrac { { x }^{ 3 }+x+1 }{ { x }^{ 2 }-1 }  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
Evaluate: $$\displaystyle \int_{-{a}}^{{a}}\{{f}({x})+{f}(-{x})\}{d}{x}$$ 
  • A. $$2\int_{0}^{a}f(x)dx$$
  • B. $$0$$
  • C. $$\displaystyle \int_{0}^{\mathrm{a}} f(-x)dx$$
  • D. $$2\displaystyle \int_{0}^{{a}}\{{f}({x})+{f}(-{x})\}{d}{x}$$ 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Medium
Value of $$ \displaystyle \int_{1}^{5} \left(\sqrt {x+2\sqrt {x-1}}+\sqrt {x-2(x-1)}\right)dx$$ is
  • A. $$\dfrac {16}{3}$$
  • B. $$\dfrac {32}{3}$$
  • C. $$\dfrac {34}{3}$$
  • D. $$\dfrac {8}{3}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Evaluate the definite integral    $$\displaystyle \int_0^{\frac {\pi}{4}}\frac {\sin x \cos x}{\cos^4 x+\sin^4x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 TRUE/FALSE Medium
If $$f,g,h$$ be continuous functions on $$[0,a]$$ such that $$f(a-x)=-f(x),g(a-x)=g(x)$$ and $$3h(x)-4h(a-x)=5$$ then  $$\displaystyle \int_0^a f(x)g(x)h(x)dx=0$$
  • A. False
  • B. True

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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