# an integral problem

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• Nov 24th 2006, 01:57 AM
oahsen
an integral problem
hi. i have a question which is the thomas calculus at chapter 5 additional exercises. can you help me i could not solve it ;

find f(pi/2) if the area under the curve y=f(x) from x=0 to x=a is ;

((a^2)/2) + (a*sin(a))/2 + (pi*cos(a))/2 ;

how should i think in order to solve this. please help me...
• Nov 24th 2006, 02:50 AM
CaptainBlack
Quote:

Originally Posted by oahsen
hi. i have a question which is the thomas calculus at chapter 5 additional exercises. can you help me i could not solve it ;

find f(pi/2) if the area under the curve y=f(x) from x=0 to x=a is ;

((a^2)/2) + (a*sin(a))/2 + (pi*cos(a))/2 ;

how should i think in order to solve this. please help me...

Fundamental theorem of calculus:

$
f(x)=\frac{d}{dx}\int_0^x f(\zeta) d \zeta
$

so:

$
f(x)=\frac{d}{dx}\ [x^2/2 + x\ \sin(x)/2 + \pi\ \cos(x)/2]
$

RonL
• Nov 24th 2006, 06:00 AM
oahsen
i understood thanks a lot