Find \int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx.

Category: QuestionsFind \int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx.
Editor">Editor Staff asked 11 months ago

Find \int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx.
(a) -5
(b) 9
(c) 5
(d) -9
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The above asked question is from Fundamental Theorem of Calculus-1 topic in chapter Integrals of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct answer is (c) 5
The best explanation: Let I=\int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx
F(x)=\int5 \,sin⁡x \,dx=-5 \,cos⁡x
Applying the limits by using the fundamental theorem of calculus, we get
∴\int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx=-5[cos⁡\frac{π}{2}-cos⁡0]