What is the integral from 4 to 9 of 2sqrt(x)(10x+3) ?

The integral from 4 to 9 of 2sqrt(x)(10x+3) is 1764

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integral from 4 to 9 of 2sqrt(x)(10x+3)

\int_{4}^{9} 2 x (10 x + 3) d x

1764

Solution steps

\int_{4}^{9} 2 x (10 x + 3) d x

Take the constant out:

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

= 2 \cdot \int_{4}^{9} x (10 x + 3) d x

Expand

x (10 x + 3) : 10 x^{\frac{3}{2}} + 3 x

= 2 \cdot \int_{4}^{9} 10 x^{\frac{3}{2}} + 3 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int_{4}^{9} 10 x^{\frac{3}{2}} d x + \int_{4}^{9} 3 x d x)

\int_{4}^{9} 10 x^{\frac{3}{2}} d x = 844

\int_{4}^{9} 3 x d x = 38

= 2 (844 + 38)

Simplify

= 1764

What is the integral from 4 to 9 of 2sqrt(x)(10x+3) ?
The integral from 4 to 9 of 2sqrt(x)(10x+3) is 1764