Let Fx be the primitive of 3x-2-x-9 with respect to x- If F10 - 60- then the value of F13 is

F(x) = ∫3x+2√(x 9) dx Put x 9 = t^2 ⇒ dx = 2t dt ∴ F(x) =∫( 3(t^2+9)+2t)·2t dt = 2∫(29 + 3t^2) dt nbsp;= 2(29t + t^3)+C F(x) = 2 [ 29 √(x 9) + (x 9)^3/2] +C ...

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Byju's Answer

Standard XII

Mathematics

Constant Function

Let Fx be the...

Question

Let $F (x)$ be the primitive of $\frac{3 x + 2}{\sqrt{x - 9}}$ with respect to $x$ . If $F (10) = 60,$ then the value of $F (13)$ is

132

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132.0

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132.00

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Solution

$F (x) = \int \frac{3 x + 2}{\sqrt{x - 9}} d x$
Put $x - 9 = t^{2}$
$\Rightarrow d x = 2 t d t$
$∴ F (x) = \int (\frac{3 (t^{2} + 9) + 2}{t}) \cdot 2 t d t$
$= 2 \int (29 + 3 t^{2}) d t = 2 (29 t + t^{3}) + C$
$F (x) = 2 [29 \sqrt{x - 9} + (x - 9)^{3 / 2}] + C$
As $F (10) = 60, C = 0$
$∴ F (x) = 2 [29 \sqrt{x - 9} + (x - 9)^{3 / 2}]$
$F (13) = 2 (58 + 8) = 132$

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Let F(x) be the primitive of 3x+2√x−9 with respect to x. If F(10)=60, then the value of F(13) is

F(x)=∫3x+2√x−9dx Put x−9=t2 ⇒dx=2t dt ∴F(x)=∫(3(t2+9)+2t)⋅2t dt =2∫(29+3t2)dt=2(29t+t3)+C F(x)=2[29√x−9+(x−9)3/2]+C As F(10)=60, C=0 ∴F(x)=2[29√x−9+(x−9)3/2] F(13)=2(58+8)=132

Let $F (x)$ be the primitive of $\frac{3 x + 2}{\sqrt{x - 9}}$ with respect to $x$ . If $F (10) = 60,$ then the value of $F (13)$ is