# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_{0}^{4}\left(\sqrt{16-x^2}-\frac{1}{8}\cdot\left(16-x^2\right)\right)dx$

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

$\int_{0}^{4}\sqrt{16-x^2}dx+\int_{0}^{4}-\frac{1}{8}\left(16-x^2\right)dx$

Learn how to solve definite integrals problems step by step online. Integrate (16-x^2)^0.5-1/8*(16-x^2) from 0 to 4. The integral of a sum of two or more functions is equal to the sum of their integrals. The integral \int_{0}^{4}\sqrt{16-x^2}dx results in: 4\pi . The integral \int_{0}^{4}-\frac{1}{8}\left(16-x^2\right)dx results in: -5.3333. Gather the results of all integrals.

$7.233$

### Problem Analysis

$\int_{0}^{4}\left(\sqrt{16-x^2}-\frac{1}{8}\cdot\left(16-x^2\right)\right)dx$

### Main topic:

Definite integrals

~ 0.2 seconds