1.

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»

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

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


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