Mathematics

If $$I_{1}=\displaystyle \int{\sin^{-1}xdx}$$ and $$I_{2}=\displaystyle \int{\sin^{-1}\sqrt{1-x^{2}}xdx}$$ then


ANSWER

$$I_{1}=I_{2}$$


View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
The value of$${\smallint _{100}}{1000}\frac{{dx}}{x}is$$
  • A. $$10$$
  • B. $$1$$
  • C. $$2.303$$
  • D. $$4.606$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
Evaluate the following definite integrals as limit of sums.
$$\displaystyle\int^{1}_{-1}e^xdx$$.
  • A. $$e^2-1$$
  • B. $$\dfrac{e^2-1}{2}$$
  • C. $$\dfrac{e^2-1}{e^2}$$
  • D. $$\dfrac{e^2-1}{e}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
Evaluate $$\displaystyle\int{\frac{dx}{{(x^2+a^2)}^3}}$$.
  • A. $$\displaystyle I=\frac{x}{2a^2{(x^2+a^2)}^2}+\frac{3}{4a^2}\left\{\frac{x}{a^2(x^2+a^2)}+\frac{1}{a^3}\tan^{-1}{\left(\frac{x}{a}\right)}\right\}+C$$
  • B. $$\displaystyle I=\frac{x}{4a^2{(x^2+a^2)}^2}+\frac{1}{4a^2}\left\{\frac{x}{2a^2(x^2+a^2)}+\frac{1}{2a^3}\sec^{-1}{\left(\frac{x}{a}\right)}\right\}+C$$
  • C. $$\displaystyle I=\frac{x}{a^2{(x^2+a^2)}^2}+\frac{3}{2a^2}\left\{\frac{x}{2a^2(x^2+a^2)}+\frac{1}{2a^3}\tan^{-1}{\left(\frac{x}{a}\right)}\right\}+C$$
  • D. $$\displaystyle I=\frac{x}{4a^2{(x^2+a^2)}^2}+\frac{3}{4a^2}\left\{\frac{x}{2a^2(x^2+a^2)}+\frac{1}{2a^3}\tan^{-1}{\left(\frac{x}{a}\right)}\right\}+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium

$$\displaystyle \int_{0}^\frac{\pi}{2}\frac{dx}{1+\tan x}=$$
  • A. $$\displaystyle \frac{\pi}{2}$$
  • B. $$1$$
  • C. $$\log 2$$
  • D. $$\displaystyle \frac{\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Let $$n \space\epsilon \space N$$ & the A.M., G.M., H.M. & the root mean square of $$n$$ numbers $$2n+1, 2n+2, ...,$$ up to $$n^{th}$$ number are $$A_{n}$$, $$G_{n}$$, $$H_{n}$$ and $$R_{n}$$ respectively. 
On the basis of above information answer the following questions

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer