Calculus Examples

$\int_{0}^{4 π} 5 \sin (x^{2}) d x$

Step 1

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int_{0}^{4 π} \sin (x^{2}) d x$

Step 2

$\int_{0}^{4 π} \sin (x^{2}) d x$ is a special integral. The integral is the Fresnel integral function.

$5 (S (x)]_{0}^{4 π})$

Step 3

Substitute and simplify.

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Step 3.1

Evaluate $S (x)$ at $4 π$ and at $0$ .

$5 ((S (x)) - S (x))$

Step 3.2

Simplify.

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Step 3.2.1

Subtract $S (x)$ from $S (x)$ .

$5 \cdot 0$

Step 3.2.2

Multiply $5$ by $0$ .

$0$