Evaluate the integral \int_1^5x^2 \,dx.

Category: QuestionsEvaluate the integral \int_1^5x^2 \,dx.
Editor">Editor Staff asked 11 months ago

Evaluate the integral \int_1^5x^2 \,dx
.
 
(a) \frac{125}{3}
 
 
(b) \frac{124}{3}
 
 
(c) 124
 
(d) –\frac{124}{3}
 
 
This question was addressed to me in unit test.
 
My question is taken from Fundamental Theorem of Calculus-2 topic in portion Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Right option is (b)
124
3
 
 
To elaborate: Let I=

5
1
x
2
dx
 
 
F(x)=

x
2
dx
 
 
=
x
3
3
 
 
By using the fundamental theorem of calculus, we get
 
I=F(5)-F(1)
 
=
5
3
3

1
3
3
=
125−1
3
=
124
3