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12th Class Mathematics Definite Integrals Question Bank Critical Thinking

  • question_answer
    The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one of such region is [DCE 2005]

    A) \[\sqrt{2}\]                           

    B) \[2\sqrt{2}\]

    C) \[3\sqrt{2}\]                         

    D) \[4\sqrt{2}\]

    Correct Answer: B

    Solution :

    • Point of intersection of y=sinx and \[y=\cos x\]are \[\frac{\pi }{4},\] \[\frac{\pi }{4},\frac{5\pi }{4}\].           
    • Since, \[\sin x\ge \cos x\] on the interval \[\left[ \frac{\pi }{4},\frac{5\pi }{4} \right]\] \[\therefore \] Area of one such region \[=\int_{\pi /4}^{5\pi /4}{(\sin x-\cos x)\ dx}\] \[=2\sqrt{2}sq.\ unit\].


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