1.

Find \(\int_0^2 \,e^{2x} \,dx\).(a) \(\frac{e^4-1}{6}\)(b) \(\frac{e^4+1}{2}\)(c) \(\frac{e-1}{2}\)(d) \(\frac{e^4-1}{2}\)I have been asked this question in unit test.My query is from Fundamental Theorem of Calculus-1 in portion Integrals of Mathematics – Class 12

Answer»

Right ANSWER is (d) \(\frac{e^4-1}{2}\)

To ELABORATE: LET \(I=\int_0^2 \,e^2x \,dx\)

F(X)=\(\int e^{2x} dx\)

=\(\frac{e^{2x}}{2}\)

Applying the limits, we get

I=F(2)-F(0)

=\(\frac{e^2(2)}{2}-\frac{e^2(0)}{2}=\frac{(e^4-1)}{2}\).


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