What is the integral from-2x to 2x of sqrt(3x+y) ?

The integral from-2x to 2x of sqrt(3x+y) is ((10sqrt(5)-2)x^{3/2})/3

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integral from-2x to 2x of sqrt(3x+y)

\int_{- 2 x}^{2 x} 3 x + y d y

\frac{( 10 5 - 2 ) x ^{\frac{3}{2}}}{3}

Solution steps

\int_{- 2 x}^{2 x} 3 x + y d y

Apply u-substitution

= \int_{x}^{5 x} u d u

Apply the Power Rule

= [\frac{2}{3} u^{\frac{3}{2}}]_{x}^{5 x}

Compute the boundaries:

\frac{10 5 - 2}{3} x^{\frac{3}{2}}

= \frac{10 5 - 2}{3} x^{\frac{3}{2}}

Simplify

= \frac{( 10 5 - 2 ) x ^{\frac{3}{2}}}{3}

What is the integral from-2x to 2x of sqrt(3x+y) ?
The integral from-2x to 2x of sqrt(3x+y) is ((10sqrt(5)-2)x^{3/2})/3