Mathematics: I need help evaluating integrals

9x3=?9x3=27In all, Alisa has 27 pictures....

I need help evaluating integrals

Ответ:

mil3ndy

22.01.2022

Mathematics

b) 360

c) -108

d) 72

Step-by-step explanation:

b) from 0 to 30, we have a 2 trapezoids' areas to solve.

trapezoid 1: from 0 to 12

A1 = 144, given by part a

A2 = (6+18)(18)/2 = 216

144 + 216 = 360

$\int\limits^{30}_{0} {f(x)} \, dx = 360$

c) integral from 30 to 42 is just a triangle whose area will be negative since the y is negative

A = xy/2 = 12(-18)/2 = -108

$\int\limits^{42}_{30} {f(x)} \, dx = -108$

d) $\int\limits^{54}_{0} {f(x)} \, dx =$ $\int\limits^{30}_{0} {f(x)} \, dx$ $+ \int\limits^{42}_{30} {f(x)} \, dx + \int\limits^{54}_{42} {f(x)} \, dx$

$\int\limits^{54}_{0} {f(x)} \, dx =$ 360-108 + (-18 - 12)(12)/2 = 360-108-180 = 72

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I need help evaluating integrals

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