Question

Find \(\int_3^45x^3 \,dx\).

(a) –\(\frac{185}{4}\)

(b) –\(\frac{185}{3}\)

(c) \(\frac{185}{2}\)

(d) \(\frac{185}{4}\)

The question was asked by my college professor while I was bunking the class.

My question is taken from Fundamental Theorem of Calculus-2 in division Integrals of Mathematics – Class 12

Answer 1

Right answer is (d) \(\frac{185}{4}\)

The explanation is: Let \(I=\int_3^45x^3 \,dx\)

F(x)=∫ 5x^3 dx

=\(\frac{5x^4}{4}\)

Applying the limits by using the fundamental theorem of calculus, we get

I=F(4)-F(3)

=\(\frac{5(4)^3}{4}-\frac{5(3)^3}{4}=\frac{5}{4}(4^3-3^3)\)

=\(\frac{5}{4} (64-27)=\frac{5}{4} (37)=\frac{185}{4}\)