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

Find \(\int_3^45x^3 \,dx\).(a) –\(\frac{185}{4}\)(b) –\(\frac{185}

1.	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» 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) =\(\frac{5(4)^3}{4}-\frac{5(3)^3}{4}=\frac{5}{4}(4^3-3^3)\) =\(\frac{5}{4} (64-27)=\frac{5}{4} (37)=\frac{185}{4}\)

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