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+2 votes
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$\int_{-4}^{4}|3-x|dx$

a) 13 b)8  c)25  d)24
asked in Calculus by Loyal (4.9k points) | 82 views

3 Answers

+3 votes

Graphical method is easier. Graph of $\left | 3-x \right |$ is as follows : 

We just need to find area of the shaded portion, it is nothing but area of two triangles.

For larger triangle, base = 7, height = 7 $\therefore$ Area A1 = $\frac{1}{2}*7*7 = \frac{49}{2}$

For smaller triangle, base = 1, height = 1 $\therefore$ Area A2 = $\frac{1}{2}*1*1 = \frac{1}{2}$

Total required area = A1 + A2  = $\frac{49}{2} + \frac{1}{2} = 25$

answered by Veteran (11k points)
edited by
+1 vote

$\int_{-4}^{3} (3-x)dx +\int_{3}^{4} -(3-x)dx$

 

solve it you will get the answer 25

answered by Active (1.2k points)
0 votes

Since this is a definite integral , there is no question of generation of a constant as a result of integration. 

Integrating , we get (3x-x2/2)

=> 3{4-(-4)} - {(4^2)/2-(-4^2)/2}

=> 3*8 - 0 = 24 

answered by Active (1.3k points)
given answer is 25 , they used the graph method which i didnt understand
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