f i n d find I I

Calculus Level 2

I = ∫ 0 2 1 1 + x 4 I = \displaystyle\int_{0}^{\sqrt{2}} \dfrac{1}{ 1 + x^{4}} d x dx

find I I


The answer is 1.

Moaj Ahmed by Moaj Ahmed , 25, Bangladesh

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3 solutions

Lu Chee Ket
Feb 1, 2015

1.00379566691771 is the exact answer correct to 15 S.F.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Incredible Mind
Feb 6, 2015

i used 1+x^4 = (x^2 + i)(x^2-i) .then partial fractions (i is iota=sqrt-1)

1 Helpful 0 Interesting 0 Brilliant 0 Confused
. .
Apr 30, 2021

It is always 1 1 .

I = ∫ 0 2 1 1 + x 4 d x = 1 \displaystyle I = \int ^ { \sqrt { 2 } } _ { 0 } \frac { 1 } { 1 + x ^ { 4 } } dx = 1 .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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