Answer in Calculus for Aarmandi #120610

Question #120610

Find the area bounded by the curve y = |x−1|, the x-axis and the lines x = −7 and x = 11

Expert's answer

$\text{As shown in the figure},\\ \text{ the area is divided to parts}\\ A=\int\limits_{-7}^1(-x+1-0)dx+\int\limits_1^{11}(x-1-0)dx\\ =\int\limits_{-7}^1(-x+1)dx+\int\limits_1^{11}(x-1)dx\\ =(-x^2/2+x)|_{-7}^1+(x^2/2-x)|_1^{11}\\ =-0.5+1+49/2+7\\ +121/2-11-0.5+1\\ =82$

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Comments

Assignment Expert

10.06.20, 22:43

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Tiyiselani

10.06.20, 17:03

Thanks!!

Assignment Expert

10.06.20, 00:04

Since the function y=|x-1| has different signs on x1, area as the definite integrals should be considered for these two cases separately. The bounds a=-7, b=1 were chosen because x1 was considered and the curve is bounded by the line x=11.

aarmandi

09.06.20, 03:28

HI. Since we know that we are given the value a=-7 and b=11, do we just assume that since were not given a b for both integrals, we will then evaluate by 1, b=-7 and a=1, 11