Find the value \int_{-1}^23x+x^2-2 \,dx.

Category: QuestionsFind the value \int_{-1}^23x+x^2-2 \,dx.
Editor">Editor Staff asked 11 months ago

Find the value \int_{-1}^23x+x^2-2 \,dx.
(a) –\frac{4}{3}
(b) \frac{3}{2}
(c) \frac{5}{6}
(d) –\frac{5}{6}
The question was posed to me during an online exam.
This intriguing question comes from Fundamental Theorem of Calculus-2 topic in portion Integrals of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (b) \frac{3}{2}
Easiest explanation: Let I=\int_{-1}^23x+x^2-2 \,dx
F(x)=\int 3x+x^2-2 \,dx
Applying the limits, we get
I=\left(\frac{(3×2^3)}{2}+\frac{2^3}{3}-2(2)\right)-\left(\frac{3 (-1)^2}{2}+\frac{(-1)^3}{3}-2(-1)\right)