# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_{0}^{2}\left(\frac{5}{2}\pi^2 z^2+3\pi\cdot y\cdot \cos\left(z\right)\right)dy$

Learn how to solve definite integrals problems step by step online.

$\int_{0}^{2}24.674z^2dy+\int_{0}^{2}3\pi y\cos\left(z\right)dy$

Learn how to solve definite integrals problems step by step online. Integrate 24.674011002723397z^2+9.42477796076938y*cos(z) from 0 to 2. The integral of a sum of two or more functions is equal to the sum of their integrals. The integral \int_{0}^{2}24.674z^2dy results in: 49.348z^2. The integral \int_{0}^{2}3\pi y\cos\left(z\right)dy results in: 6\pi \cos\left(z\right). Gather the results of all integrals.

$49.348z^2+6\pi \cos\left(z\right)$
$\int_{0}^{2}\left(\frac{5}{2}\pi^2 z^2+3\pi\cdot y\cdot \cos\left(z\right)\right)dy$

### Main topic:

Definite integrals

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### Time to solve it:

~ 0.06 s (SnapXam)