Let f(x) be a continous function such that its first two derivatives f'(x) and f''(x) are continous. The tangents to the graph of f(x) at the points with abscissa x=a and x=b make with the X-axies angles π / 3 and π /4 respectively. then the value of the integral
Integrate [ f'(x) * f''(x) dx ] from a to b equals?
But please next time, write down what you've tried;...
Now you know that the tangent to the curve at point a, has a slope of f'(a).
If it forms an angle of pi/3 with the x axis, it means that its slope is tan(pi/3) ---> f'(a)=tan(pi/3) and f'(b)=tan(pi/4)
There is an example here : Vectors Aligned with X-Y Axes, but I can't find a good link (and it's time to eat ^^)