Question
Calculate ∫3−2f(x)dx where
f(x)={6ifx>13x2ifx≤1
f(x)={6ifx>13x2ifx≤1
Answer: Option B
:
B
Here, we can see that the integrand f(x) in not continuous in the interval (-2, 3) as it has a discontinuity at x = 1. So we can’t just integrate f(x) and put limits.We’ll have to break this integral into integrals which have limits such that integrands is continuous in those limits.
∫3−2f(x)dx=∫1−23x2dx+∫316dx
Now we can integrate these integrands and put limits.
∫1−23x2dx+∫316dx=(x3)|1−2+(6x)|31=1−(−8)+18−6
= 21
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:
B
Here, we can see that the integrand f(x) in not continuous in the interval (-2, 3) as it has a discontinuity at x = 1. So we can’t just integrate f(x) and put limits.We’ll have to break this integral into integrals which have limits such that integrands is continuous in those limits.
∫3−2f(x)dx=∫1−23x2dx+∫316dx
Now we can integrate these integrands and put limits.
∫1−23x2dx+∫316dx=(x3)|1−2+(6x)|31=1−(−8)+18−6
= 21
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