Step-by-step Solution

Integrate $\sqrt{16-x^2}-\left(\frac{1}{8}\right)\left(16-x^2\right)$ from $0$ to $4$

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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.

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

Unlock this full step-by-step solution!

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.

Final Answer

$7.233$

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

Related formulas:

5. See formulas

Time to solve it:

~ 0.2 seconds