What is the integral from 0 to 4 of 4x ?

The integral from 0 to 4 of 4x is 32

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integral from 0 to 4 of 4x

\int_{0}^{4} 4 x d x

32

Solution steps

\int_{0}^{4} 4 x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{0}^{4} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{4}

= 4 [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= 4 \cdot 8

Simplify

= 32

\int \frac{sin ( x )}{( 1 + cos ( x ) ) ^{3}} d x

x^{^{''}} = 0

\int cos^{5} (x) sin (x) d x

\frac{d}{d x} (x ln (x + 2))

y^{^{''}} + 16 y = 1 + 2 sin (4 x)