Question

Integrate with respect to x :
∫2−2(x3−3x2+2x−5)dx

a -36
b 35
c 40
d 41

Answer 1

Answer on Question #50922 – Math – Integral Calculus

Integrate with respect to $x$ :

$$\int_{-2}^{2} (x^3 - 3x^2 + 2x - 5) \, dx$$

a. -36

b. 35

c. 40

d. 41

Solution

Apply Newton-Leibniz formula and table integral for the power function:

$$\begin{aligned} \int_{-2}^{2} (x^3 - 3x^2 + 2x - 5) \, dx &= \left(\frac{x^4}{4} - x^3 + x^2 - 5x\right) \Big|_{-2}^{2} = \\ &= \left(\frac{16}{4} - 8 + 4 - 10\right) - \left(\frac{16}{4} + 8 + 4 + 10\right) = -36 \end{aligned}$$

Thus, the answer is a, that is, -36.

**Answer**: -36.

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