1.

Find \(\int_{-1}^1 \,2xe^x \,dx\).(a) \(\frac{4}{e}\)(b) 4e(c) –\(\frac{4}{e}\)(d) -4eThis question was posed to me in my homework.I would like to ask this question from Fundamental Theorem of Calculus-1 in section Integrals of Mathematics – Class 12

Answer»

The correct choice is (a) \(\FRAC{4}{e}\)

To elaborate: \(I=\int_{-1}^1 \,2xe^X \,dx\)

F(x)=\(\int 2xe^x dx\)

By using the formula, \(\int U.v \,dx=u \int v \,dx-\int u'(\int v \,dx)\)

F(x)=2x\(\int e^x dx-\int(2x)’\int e^x \,dx\)

=\(2xe^x-\int 2e^x dx\)

=\(2e^x (x-1)\)

Therefore, by using the fundamental theorem of calculus, we get

I=F(1)-F(-1)

I=2e^1 (1-1)-2e^-1 (-1-1)

I=\(\frac{4}{e}\).


Discussion

No Comment Found

Related InterviewSolutions