Mathematics

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

Q1 Single Correct Medium
If $${ I }_{ n }=\int { \sin ^{ n }{ x } dx },$$, then $${ nI }_{ n }-\left( n-1 \right) { I }_{ n-2 }=$$
  • A. $$\sin ^{ n-1 }{ x\cos { x } }$$
  • B. $$\cos ^{ n-1 }{ x\sin{ x } }$$
  • C. $$-\cos ^{ n-1 }{ x\sin{ x } }$$
  • D. $$-\sin ^{ n-1 }{ x\cos { x } }$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Medium
$$\displaystyle \int\dfrac{{1-x^{}}}{1+x^{2}}$$ dx

Asked in: Mathematics - Integrals


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Q3 Subjective Medium
$$I = \int {{{{x^2}} \over {\sqrt {1 - {x^6}} }}dx} $$

Asked in: Mathematics - Integrals


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Q4 Single Correct Medium
$$\displaystyle \int x^{3}\tan ^{-1}x\:dx.$$
  • A. $$\displaystyle \frac{1}{2}\left [ \left ( x^{4}-1 \right )\tan ^{-1}x-\frac{x^{2}}{3}+x \right ].$$
  • B. $$\displaystyle \frac{1}{2}\left [ \left ( x^{4}+1 \right )\tan ^{-1}x-\frac{x^{2}}{3}+x \right ].$$
  • C. $$\displaystyle \frac{1}{4}\left [ \left ( x^{4}-1 \right )\tan ^{-1}x-\frac{x^{1}}{3}+x \right ].$$
  • D. $$\displaystyle \frac{1}{4}\left [ \left ( x^{4}-1 \right )\tan ^{-1}x-\frac{x^{2}}{3}+x \right ].$$

Asked in: Mathematics - Integrals


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Q5 Passage Hard
Let $$g(x)$$ be a function defined on $$[0, 7]$$ and $$g(x)=\int_0^x f(t) dt$$, where $$y=f(x)$$ is the function whose graph is as shown in figure given below, then

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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