InterviewSolution
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InterviewSolution
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Evaluate the integral \(\int_0^{\frac{π^2}{4}} \frac{9 sin\sqrt{x}}{2\sqrt{x}} dx\).(a) 9(b) -9(c) \(\frac{9}{2}\)(d) –\(\frac{9}{2}\)This question was posed to me in examination.The above asked question is from Evaluation of Definite Integrals by Substitution in section Integrals of Mathematics – Class 12 |
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Answer» RIGHT answer is (a) 9 The EXPLANATION: I=\(\int_0^{\frac{π^2}{4}} \frac{9 sin\SQRT{x}}{2\sqrt{x}} dx\) Let \(\sqrt{x}\)=t Differentiating both sides w.r.t x, we GET \(\frac{1}{2\sqrt{x}} dx=dt\) The new limits are When x=0 , t=0 When x=\(\frac{π^2}{4}, t=\frac{π}{2}\) ∴\(\int_0^{\frac{π^2}{4}} \frac{9 sin\sqrt{x}}{2\sqrt{x}} dx=9\int_0^{π/2} sint \,dt\) =\(9[-cost]_0^{π/2}\)=-9(cos π/2-cos0)=-9(0-1)=9 |
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