Q64 / 150 · MHT CET 2009 · Mathematics

Which of the following is true?

  • A
    $\int_{0}^{1} e^{x} d x=e$
  • B
    $\int_{0}^{1} 2^{x} d x=\log 2$
  • Correct answer
    C
    $\int_{0}^{1} \sqrt{x} d x=\frac{2}{3}$
  • D
    $\int_{0}^{1} x d x=\frac{1}{3}$

Solution

$\int_{0}^{1} e^{x} d x=\left[e^{x}\right]_{0}^{1}=e-1$ (b) $\int_{0}^{1} 2^{x} d x=\left[\frac{2^{x}}{\log _{e} 2}\right]_{0}^{1}=\frac{1}{\log 2} \cdot\left(2-2^{0}\right)=\frac{1}{\log 2}$ (c) $\int_{0}^{1} \sqrt{x} d x=\left[\frac{x^{3 / 2}}{3 / 2}\right]_{0}^{1}=\frac{2}{3}$ (d) $\int_{0}^{1} x d x=\left[\frac{x^{2}}{2}\right]_{0}^{1}=\frac{1}{2}$

Hence, the correct answer is option: 'C'.

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