Thread: find area under the curve using calculus

hi
how are u all
i have a math problem that require from
me to find area under the curve
but because am not good in math i didn't
understand how to find the expresion in the blue
rectangle
in the attached pic


upload picture

any help
is appreciated ...


secondly ...to make sure i will understand this
type of problems and how to solve it,
could any one plz solve for me the problem
below(find tha area under curve)
and thanks in advance

There is no 'finding' , that is an arbitrary choice. Once you have divided the interval 0 to 1 in n subintervals, each having length , and so right endpoints , , , ..., , ..., you must choose one x in each interval. Here they have just chosen the simplest- the midpoint: . You could as easily have chosen or or , etc.

In the last problem, all of the individual areas are rectangles or trapezoids. Do you know the formulas for area of a rectangle or trapezoid? Find the area of each and add them.

Originally Posted by HallsofIvy

There is no 'finding' , that is an arbitrary choice. Once you have divided the interval 0 to 1 in n subintervals, each having length , and so right endpoints , , , ..., , ..., you must choose one x in each interval. Here they have just chosen the simplest- the midpoint: . You could as easily have chosen or or , etc.

In the last problem, all of the individual areas are rectangles or trapezoids. Do you know the formulas for area of a rectangle or trapezoid? Find the area of each and add them.

hi
thanks for your help HallsofIvy
i will tray and solve as described
thanks again

Basically just divide the region into a bunch of rectangles/trapezoids as HallsofIvy said. No calculus needed.

However, if you want the exact area under the curve, say , then you'd need an integral, , which is equal to 1/3.