JEE Main & Advanced Mathematics Definite Integration Question Bank Self Evaluation Test - Application of Integrals

  • question_answer
    What is the area of the portion of the curve\[y=sin\text{ }x\], lying between \[x=0,\text{ }y=0\] and\[x=2\pi \]?

    A) 1 square unit

    B) 2 square units

    C) 4 square units

    D) 8 square units

    Correct Answer: B

    Solution :

    [b] Required area \[=\int\limits_{0}^{2\pi }{\sin \,\,x\,\,dx}\] \[=-\cos \left. x \right|_{0}^{2\pi }=-\cos 2\pi -(-\cos 0)\] \[=-\cos (\pi +\pi )+1=-\,\,[-\cos \pi ]+1\] \[=+\cos \left( \frac{\pi }{2}+\frac{\pi }{2} \right)+1\] \[=\sin \frac{\pi }{2}+1=1+1=2\] sq. units.


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