Question

If q(v) = integrate sqrt(4 + w ^ 5) dw from 0 to pi ^ 1 * tren; q^ prime (v)=

Answer 1

Given:

$q(v)=\int_0^{v^7}\sqrt{4+w^5}dw$

Required:

We need to find q'(v).

Explanation:

Consider the given equation.

$q(v)=\int_0^{v^7}\sqrt{4+w^5}dw$$q(v)=\int_0^{v^7}\sqrt{4+w^5}\times\frac{\sqrt{4+w^5}}{\sqrt{4+w^5}}dw$$q(v)=\int_0^{v^7}\frac{4+w^5}{\sqrt{4+w^5}}dw$$We\text{ know that d\lparen}\sqrt{4+w^5})=\frac{1}{2}\frac{1}{\sqrt{4+w^5}}5w^4dw.$$\frac{2}{5w^4}\text{ d\lparen}\sqrt{4+w^5})=\frac{1}{\sqrt{4+w^5}}dw.$

The given integral can be written as follows.

$q(v)=\int_0^{v^7}(4+w^5)\frac{2}{5w^4}d(\sqrt{4+w^5})$$q(v)=\frac{2}{5}\int_0^{v^7}\frac{(4+w^5)}{w^4}d(\sqrt{4+w^5})$$q(v)=\frac{2}{5}\int_0^{v^7}\frac{(\sqrt{4+w^5})^2}{w^4}d(\sqrt{4+w^5})$