How to calculate the integral <msubsup> &#x222B;<!-- ∫ --> <mrow class="MJX-TeXAtom-OR

hawatajwizp

hawatajwizp

Answered question

2022-06-26

How to calculate the integral 0.5 1 1 2 x x 2 ?

Answer & Explanation

Marlee Guerra

Marlee Guerra

Beginner2022-06-27Added 25 answers

Note that
2x-x2=1-(1-2x+x2)=1-(1-x)2
Now you can use a trig substitution.
minwaardekn

minwaardekn

Beginner2022-06-28Added 6 answers

Given 0.5 1 1 2 x x 2 d x
= 1 1 ( x 1 ) 2 d x
Apply u substitution u=x-1
1 1 u 2 d u = arcsin ( u ) = arcsin ( x 1 )
Now apply the boundaries
= [ arcsin ( x 1 ) ] 0.5 1 = π 6

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?