Calculus Examples

$\int_{4}^{7} f (x) d x + \int_{2}^{4} f (x) d x$

Step 1

By the Sum Rule, the derivative of $\int_{4}^{7} f (x) d x + \int_{2}^{4} f (x) d x$ with respect to $x$ is $\frac{d}{d x} [\int_{4}^{7} f (x) d x] + \frac{d}{d x} [\int_{2}^{4} f (x) d x]$ .

$\frac{d}{d x} [\int_{4}^{7} f (x) d x] + \frac{d}{d x} [\int_{2}^{4} f (x) d x]$

Step 2

Since $\int_{4}^{7} f (x) d x$ is constant with respect to $x$ , the derivative of $\int_{4}^{7} f (x) d x$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [\int_{2}^{4} f (x) d x]$

Step 3

Since $\int_{2}^{4} f (x) d x$ is constant with respect to $x$ , the derivative of $\int_{2}^{4} f (x) d x$ with respect to $x$ is $0$ .

$0 + 0$

Step 4

Add $0$ and $0$ .

$0$