Question

if f(x) integral of tan^2x sec^2 xdx and f(0) equals 3, find f(pi/4)

Answer 1

The point (3,2) is on curve and at any pt. (x,y)on the curve, the tangent line has a slope equal to 2x-3. Find the equation of the curve.

Answer 2

f(x) = ∫tan^2x sec^2x dx = 1/3 tan^3 x + C
f(0) = 3, so C=3 and f(x) = 1/3 tan^3 x + 3
so, f(π/4) = 1/3 + 3 = 10/3

for the second one, you have
y' = 2x-3
so, y = x^2 - 3x + C
since (3,2) is on the graph, y(3) = 2
so, plug that in to find C.