Help with C3 Integration. Watch
According to examiners report these were very hard questions and hardly anyone got full marks.
(iii) put the x value of a and c into the gradient function to get the gradient and if you times the two gradients together you should get -1.
(iv) simply integrate then substitute the cordinates of a to find +C , Now just use the x coordinate of a and substitute into the intigrated equation, this will give you the area.
Hope this helps!
For iii). multiply the gradients of either tangent together. When multiplying the gradients of perpendicular lines, you should get -1.
iv). Integrate the original y= equation you're given, remembering the proof you're given in the question. You're finding the area between the lines CD and BE, bounded by the curve and the x axis. So integrate between the two x co-ordinates, relating to point E and D. Integrate from D to E.
Regarding part iv, since there isn't a standard integral for that we know of, I suggest letting
The formula for integration by parts is
and is derived from the product rule of differentiation.