2. Solved Papers
  3. CET Karnataka Engineering

CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
    If  \[\int_{0}^{1}{f(x)\,dx=5,}\] then the value of \[....+100\int_{0}^{1}{{{x}^{9}}\,\,f({{x}^{10}})dx}\]is equal to

    A)  \[125\]                                

    B)  \[625\]

    C)  \[275\]                                

    D)  \[55\]

    Correct Answer: D

    Solution :

    Given,  \[\int_{0}^{1}{f(x)\,dx=5}\] Let \[I=100\int_{0}^{1}{{{x}^{9}}f({{x}^{10}})dx}\] Put \[{{x}^{10}}=t\Rightarrow 10{{x}^{9}}dx=dt\] \[\therefore \]  \[I=100\int_{0}^{1}{\frac{f(t)}{10}}\,\,dt\] \[=10\times 5=50\]                 \[\therefore \]  \[\int_{0}^{1}{f(x)\,dx+100\int_{0}^{1}{{{x}^{9}}f({{x}^{10}})dx}}\] \[=5+50=55\]


You need to login to perform this action.
You will be redirected in 3 sec spinner