Let F(x) be the antiderivative of $f (x) = 3 c o s x - 2 s i n x$ whose graph passes through the point $(π / 2, 1)$ Then F(0) is equal to

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Solution

$F (x) = \int f (x) d x = \int (3 c o s x - 2 s i n x) d x = 3 \int cos x d x - 2 \int sin x d x$

$F (x) = 3 sin x + 2 cos x + c$
As is passes through $(\frac{π}{2}, 1)$
$F (\frac{π}{2}) = 1$

$\Rightarrow 3 sin \frac{π}{2} + 2 cos \frac{π}{2} + c = 1$

$\Rightarrow c = - 2$
Then $F (0) = 3 sin 0 + 2 cos 0 - 2 = 2 - 2 = 0$

$∴ F (0) = 0$

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Let F(x) be the antiderivative of f(x)=3cosx−2sinx whose graph passes through the point (π/2,1) Then F(0) is equal to

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Let F(x) be the antiderivative of $f (x) = 3 c o s x - 2 s i n x$ whose graph passes through the point $(π / 2, 1)$ Then F(0) is equal to