Mathematics

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

Q1 Subjective Medium
Evaluate the given integral.
$$\int { x\cos { x }  } dx\quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
Let $$y=f(x)$$ be a continuous function such that $$(3-x)=f(3+x)\ \forall\ x\ \in\ R$$. If $$\displaystyle \int^{-2}_{-5}f(x)dx=2\int^{2}_{-2}f(x)dx=3$$ and $$\displaystyle \int^{4}_{2}f(x)dx=4$$ then the value of $$\displaystyle \int^{11}_{-5}f(x)dx$$ equals
  • A. $$16$$
  • B. $$14$$
  • C. $$12$$
  • D. $$18$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
Solve:

$$\displaystyle\int_{0}^{\pi/2}\dfrac{\sin x+\cos x}{3+\sin 2x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Hard
If $$\displaystyle I = \int \cot^{-1} \left ( \frac {a^2 - ax + x^2}{a^2} \right ) dx$$, then $$I$$ equals
  • A. $$\displaystyle x \tan^{-1} \left ( \frac {x}{a} \right ) - (x - a) \tan^{-1} \left ( \frac {x - a}{a} \right ) + C$$
  • B. $$\displaystyle \frac {a}{2} \log (2a^2 - 2ax + x^2) - \frac {a}{2} \log (x^2 + a^2) + C$$
  • C. $$\displaystyle x \tan^{-1} \left ( \frac {x}{a} \right ) + (x - a) \tan^{-1} \left ( \frac {x - a}{a} \right ) + \frac {a}{2} \log (2a^2 - 2ax + x^2) + C$$
  • D. none of these

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Passage Medium
The average value of a function f(x) over the interval, [a,b] is the number $$\displaystyle \mu =\frac{1}{b-a}\int_{a}^{b}f\left ( x \right )dx$$
The square root $$\displaystyle \left \{ \frac{1}{b-a}\int_{a}^{b}\left [ f\left ( x \right ) \right ]^{2}dx \right \}^{1/2}$$ is called the root mean square of f on [a, b]. The average value of $$\displaystyle \mu $$ is attained id f is continuous on [a, b].

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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