Question

Integrate completely with respect to x :
∫10(7−4x)2dx

a 79/3

b 14/15

c 81/70

d 16/3

Answer 1

Answer on Question #50921, Math, Integral Calculus

Task:

Integrate completely with respect to $x$:

$$\int_{0}^{1} (7 - 4x)^{2} \, dx$$

a. 79/3

b. 14/15

c. 81/70

d. 16/3

Solution:

$$\int_{0}^{1} (7 - 4x)^{2} \, dx = \int_{0}^{1} (49 - 56x + 16x^{2}) \, dx = (49x - \frac{56x^{2}}{2} + \frac{16x^{3}}{3}) \Bigg|_{0}^{1} = 49 - 28 + \frac{16}{3} = \frac{79}{3}$$

Answer: a. 79/3

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