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Home  >>  CBSE XII  >>  Math  >>  Model Papers
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If \( \int_0^1 (3x^2+2x+k)dx=0,\) find the value of k

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Toolbox:
  • $\int \limits_a^b f(x)dx=F(b)-F(a)$
  • $\int x^ndx=\Large\frac{x^{n+1}}{n+1}$
Step 1:
Let $I=\int_0^1(3x^2+2x+k)dx=0$
On integrating we get,
$\bigg[3\large\frac{x^3}{3}$$+2\large\frac{x^2}{2}$$+kx\bigg]_0^1=0$
(i.e) $\big(x^3+x^2+kx\big)_0^1=0$
Step 2:
On applying the limits we get,
$\Rightarrow [1+1+k-0]=0$
$\Rightarrow k+2=0$
$k=-2$
answered Sep 23, 2013 by sreemathi.v
 

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