integration

Question

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

a) 13 b)8  c)25  d)24

Answer 1

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  = $\frac{49}{2} + \frac{1}{2} = 25$

Answer 2

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

solve it you will get the answer 25

Answer 3

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 

Comments

given answer is 25 , they used the graph method which i didnt understand

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