What is the integral from-1 to 1 of y*sqrt(1-y^2) ?

The integral from-1 to 1 of y*sqrt(1-y^2) is 0

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integral from-1 to 1 of y*sqrt(1-y^2)

\int_{- 1}^{1} y \cdot 1 - y^{2} d y

0

Solution steps

\int_{- 1}^{1} y 1 - y^{2} d y

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

y 1 - y^{2} :

Odd

= 0

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} y d y

\int_{0}^{1} \frac{5}{2} y^{\frac{3}{2}} d y

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} x d x

\int_{1}^{π} cos (3 t) + 8 t d t

\int_{- 1}^{2} x^{2} + 2 x - x^{3} d x

What is the integral from-1 to 1 of y*sqrt(1-y^2) ?
The integral from-1 to 1 of y*sqrt(1-y^2) is 0