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HELP! finding area calculus

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Find the area between f(x) = x^3 + 2 and the x-axis from -1 to 2

Find the area between f(x) = sinx and the x axis from 0 to 3π/4

Thank youuu!

Mar 24, 2019

#1
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1. $$\text{We can use an integral: } \int^{2}_{-1}( x^3 + 2) dx = ? \text{ We now find the antiderivative of } x^3+2\\ \text{which turns out to be } \frac{1}{4} x^4 \text{. Then, we plug it in:} \frac{1}{4}(2)^4 - \frac{1}{4}(-1^4) = \frac{17}{4}.$$

2. $$\text{We use another integral: } \int^{3\pi/4}_{0} \sin x \: dx. \text{Take the antiderivative of }\sin x \text{, which is just }-\cos x. \text{Thus, the answer is }\\ -\cos(\frac{3\pi}{4}) - ( -\cos 0) = \frac{\sqrt{2}}{2} + 1.$$

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Mar 24, 2019
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