2305\int^{\sqrt{\ln \pi/2}}_{0}\cos(e^{x^{2}})2xe^{x^{}2}dx=\int^{\pi/2}_{1}\cos(e^{x^{2}})de^{x^{2}}
1-\sin1
- Shaswata Roy 2:Answer-CUpvote·0· Reply ·2013-08-14 03:37:47
7 Answers
23055)\int cot^{-1}e^{x}\cdot e^{-x}dx
-\int \tan^{-1}{e^{-x}}de^{-x}
Applying integration by parts,
-e^{-x}\tan^{-1}(e^{-x})+\frac{1}{2}\ln|e^{-2x}+1|+C
\frac{1}{2}\ln|e^{2x}+1|-x-\cot^{-1}(e^{x})e^{-x}+C
Ans-C
2305
4864) f(g(x))=x ...(1)
f'(g(x))g'(x)=1
g'(0)=1f'(g(0))
From(1)
f(g(0))=0
f(x) is zero when both upper & lower limit are equal.
f'(x)= 1√(1+x4)
f'(2)=1√17
Hence g'(0)=√17
(c)
- Niraj kumar Jha f'(x)=1/(1+x^4)^.5
