Question

Find \(\int_{π/4}^{π/2}7 \,cos⁡x \,dx\).

(a) 7(1-\(\frac{1}{\sqrt{2}}\))

(b) -7(1-\(\frac{1}{\sqrt{2}}\))

(c) 7(1+\(\frac{1}{\sqrt{2}}\))

(d) 7(\(\sqrt{2}-\frac{1}{\sqrt{2}}\))

This question was posed to me in examination.

I'd like to ask this question from Fundamental Theorem of Calculus-2 in section Integrals of Mathematics – Class 12

Answer 1

Right answer is (a) 7(1-\(\frac{1}{\sqrt{2}}\))

To explain I would say: Let \(I=\int_{π/4}^{π/2}7 \,cos⁡x \,dx\)

F(x)=∫ 7 cos⁡x dx

=7(sin⁡x)

Applying the limits by using the second fundamental theorem of calculus, we get

\(I=F(\frac{π}{2})-F(\frac{π}{4})=7(sin\frac{π}{2}-sin⁡ \frac{π}{4})=7(1-\frac{1}{\sqrt{2}})\)