Calculus Examples

$\int_{0}^{7} \sqrt{7 x} d x$

Step 1

Simplify with factoring out.

Tap for more steps...

Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x}$ as ${(7 x)}^{\frac{1}{2}}$ .

$\frac{d}{d x} [\int_{0}^{7} {(7 x)}^{\frac{1}{2}} d x]$

Step 1.2

Factor $7$ out of $7 x$ .

$\frac{d}{d x} [\int_{0}^{7} {(7 (x))}^{\frac{1}{2}} d x]$

Step 1.3

Apply the product rule to $7 (x)$ .

$\frac{d}{d x} [\int_{0}^{7} 7^{\frac{1}{2}} x^{\frac{1}{2}} d x]$

Step 2

Once $\int_{0}^{7} 7^{\frac{1}{2}} x^{\frac{1}{2}} d x$ has been evaluated, it will be constant with respect to $x$ , so the derivative of $\int_{0}^{7} 7^{\frac{1}{2}} x^{\frac{1}{2}} d x$ with respect to $x$ is $0$ .

$0$