Resolved: "Evaluate the definite integral. ∫01−2x(1−x2)5dx"

iricky827b

Answered question

2021-11-22

Evaluate the definite integral.

\int_{0}^{1} - 2 x {(1 - x^{2})}^{5} d x

Ancessitere

Beginner2021-11-23Added 17 answers

Step 1
Evaluate definite integral.
Given:

\int_{0}^{1} - 2 x {(1 - x^{2})}^{5} d x

Consider,

u = 1 - x^{2}

du=-2xdx
Step 2
Substitute in integral. We get value.

\int_{0}^{1} {(u)}^{5} d u

\Rightarrow {[\frac{u^{6}}{6}]}_{0}^{1}

\Rightarrow \frac{1}{6}

Phisecome

Beginner2021-11-24Added 18 answers

Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:

\int_{a}^{b} f (x) d x = F (x) ∣_{a}^{b} = F (b) - F (a)

Step 2: In this case,

f (x) = - 2 x {(1 - x^{2})}^{5}

. Find its integral.

\frac{{(1 - x^{2})}^{6}}{6} ∣_{0}^{1}

Step 3: Since

F (x) ∣_{a}^{b} = F (b) - F (a)

, expand the above into F(1)−F(0):

\frac{{(1 - 1^{2})}^{6}}{6} - \frac{{(1 - 0^{2})}^{6}}{6}

Step 4: Simplify.

- \frac{1}{6}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?