If -1a 3x2-2x-1 dx-36 -then the value of a is

We have, nbsp; ∫1a nbsp;3x2+2x+1 nbsp;dx=36⇒3x33+2x22+x1a=36⇒x3+x2+x1a=36⇒a3+a2+a (1+1+1)=36⇒a3+a2+a 39=0⇒a 3(a2+4a+13)=0⇒a=3 ...

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Standard XI

Mathematics

First Fundamental Theorem of Calculus

If ∫1a 3x2+2...

Question

$If \int_{1}^{a} (3 x^{2} + 2 x + 1) d x = 36, then the value of a is$

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Solution

We have,
$\int_{1}^{a} (3 x^{2} + 2 x + 1) d x = 36 \Rightarrow {(3 \frac{x^{3}}{3} + 2 \frac{x^{2}}{2} + x]}_{1}^{a} = 36 \Rightarrow {(x^{3} + x^{2} + x]}_{1}^{a} = 36 \Rightarrow (a^{3} + a^{2} + a) - (1 + 1 + 1) = 36 \Rightarrow a^{3} + a^{2} + a - 39 = 0 \Rightarrow (a - 3) (a^{2} + 4 a + 13) = 0 \Rightarrow a = 3$

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If ∫a1 (3x2+2x+1) dx=36 ,then the value of a is

We have, ∫a1 (3x2+2x+1) dx=36⇒(3x33+2x22+x]a1=36⇒(x3+x2+x]a1=36⇒(a3+a2+a)−(1+1+1)=36⇒a3+a2+a−39=0⇒(a−3)(a2+4a+13)=0⇒a=3

$If \int_{1}^{a} (3 x^{2} + 2 x + 1) d x = 36, then the value of a is$