Mathematics

Single Correct Hard Published on 17th 09, 2020
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Q1 Single Correct Hard
$$\int \sqrt{\dfrac{cos x-cos^{3} x}{1-cos^{3} x}}$$.dx is equal to


  • A. $$\dfrac{2}{3}sin^{-1}(cos^{3/2}x)+C$$
  • B. $$\dfrac{3}{2}sin^{-1}(cos^{3/2}x)+C$$
  • C. none of these
  • D. $$\dfrac{2}{3}cos^{-1}(cos^{3/2}x)+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Medium
Solve :

$$\int\limits_0^a {\dfrac{{\sqrt x }}{{\sqrt x  + \sqrt {a - x} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
Obtain: $$\int _{ a }^{ b }{ \sin { x }  } dx$$ as limit of sum.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Medium
$$\displaystyle \int e^x \sec x(1+\tan x)dx$$
  • A. $$e^x\cos x+C$$
  • B. $$e^x\sin x+C$$
  • C. $$e^x\tan x+C$$
  • D. $$e^x\sec x+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Medium
Solve :
$$\displaystyle \int_1^2(4x^3-5x^2+6x+9)dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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