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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Find the integral $\int(ax^2+bx+c)\;dx$

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Solution: $\frac{1}{3}a$$x^3$  + $\frac{1}{2}b$$x^2$ + $cx$ + $k$


$\int $$x^n$ $=$ $\frac{1}{n+1}$ $x^{n+1}$. 

Step 1: 

$\int ax^2 dx = \frac{1}{2+1} ax^{2+1} = \frac{1}{3} ax^{3}$

Step 2:

$\int bx dx = \frac{1}{1+1} bx^{1+1} = \frac{1}{2} bx^{2}$

Step 3:

$\int c dx = cx$

Step 4:

Therefore the solution is  $\frac{1}{3} ax^{3} + \frac{1}{2} bx^{2} + cx + k$

answered Dec 6, 2012 by balaji.thirumalai
edited Dec 6, 2012 by balaji.thirumalai
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