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
 
I=F(\frac{π}{2})-F(0)
 
∴\int_0^{\frac{π}{2}} \,5 \,sin⁡x \,dx=-5[cos⁡\frac{π}{2}-cos⁡0]
 
=-5[0-1]=5