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  • Need clarity, kindly explain! - Integral Calculus - JEE Main-14

Find the integral \int (7x^{2}- 5)^{14}x dx.

  • Option 1)

    \frac{(7x^{2} -5)^{15}}{15\cdot 14} + c

  • Option 2)

    \frac{(7x^{2} -5)^{15}}{15} + c

  • Option 3)

    \frac{(7x^{2} -5)^{15}}{15\cdot 7} + c

  • Option 4)

    \frac{(7x^{2} -5)^{15}}{7} + c

 

Answers (1)

best_answer

As we have learnt,

 

Extended forms of fundamental formulae -

If x is replaced by a LINEAR FUNCTION of x\Rightarrow \left ( ax+b \right ) form then ,

\int f\left ( ax+b \right )dx =\frac{F\left ( ax+b \right )}{\frac{\mathrm{d} }{\mathrm{d} x}\left ( ax+b \right )}+c

- wherein

Fundamental formulae such as   \int x^{n}dx=\frac{x^{n+1}}{n+1}  , \int sinx dx=-cosx,..... and so on 

 

 

I = \int (7x^{2}- 5)^{14}x dx

Put 7x^{2}- 5 = t \Rightarrow 14xdx = dt \Rightarrow xdx = \frac{dt}{14}

I = \frac{1}{14}\int t^{14}dt = \frac{t^{15}}{15\cdot 14} + c = \frac{(7x^{2} - 5)^{15}}{15\cdot 14} + c

 


Option 1)

\frac{(7x^{2} -5)^{15}}{15\cdot 14} + c

Option 2)

\frac{(7x^{2} -5)^{15}}{15} + c

Option 3)

\frac{(7x^{2} -5)^{15}}{15\cdot 7} + c

Option 4)

\frac{(7x^{2} -5)^{15}}{7} + c

Posted by

gaurav

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