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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

Answer»

Right option is (b) \(\frac{124}{3}\)

To elaborate: Let I=\(\int_1^5x^2 \,DX\)

F(x)=\(\INT x^2 \,dx\)

=\(\frac{x^3}{3}\)

By using the fundamental theorem of calculus, we get

I=F(5)-F(1)

=\(\frac{5^3}{3}-\frac{1^3}{3}=\frac{125-1}{3}=\frac{124}{3}\)


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