Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by trigonometric substitution
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Solve the product $-\frac{1}{8}\left(16-x^2\right)$
Learn how to solve definite integrals problems step by step online.
$\int_{0}^{4}\left(\sqrt{16-x^2}-2+\frac{1}{8}x^2\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (16-x^2)^1/2-1/8(16-x^2) from 0 to 4. Solve the product -\frac{1}{8}\left(16-x^2\right). Expand the integral \int_{0}^{4}\left(\sqrt{16-x^2}-2+\frac{1}{8}x^2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\sqrt{16-x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above.