# calculus

posted by .

calculate the area bounded between the parabola y=x2, the straight line y=(x/2)+2, line x=1 and the y-axis.

• calculus -

make a sketch to see that in your region the straight line lies above the parabola.
Find the intersection:
x^2= x/2 + 2
2x^2 - x - 4 = 0
x = appr 1.686 or x = -1.183

so we want:
Area = [integral] (x/2 + 2 - x^2) dx from 0 to 1.686
= (1/4)x^2 + 2x - (1/3)x^3 from 0 to 1.686
= ...

I will let you do the arithmetic.

## Similar Questions

1. ### Calc.

Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, …
2. ### calculus

find the volume generated of the region bounded by the parabola y=x^2 and the line y=b when revolved (b>0): a.) about the x-axis b.) about the line y=-1 c.) about the line y=a, where a>b
3. ### calculus

Find the area of the region bounded by the parabola y=x^2 , the tangent line to this parabola at (10, 100), and the x-axis.
4. ### calculus

Consider the straight line: y=1x+3. Calculate the area UNDER this line which is bounded by y=0, x=8 and x=15. (That is, the area from the horizontal axis (y=0) to the line, between the values of x=8 and x=15.) Give you answer to the …
5. ### calculous

Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.
6. ### calculous

Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.
7. ### Calculus

This is another textbook number that doesn't have the solution and I can't figure it out. Any tips would be greatly appreciated. For each of the plane surfaces, calculate the exact surface area. (Answer in fractions) (a)The surface …
8. ### Calculus

Find the volume of the solid generated by revolving the region bounded by the line y=5x+6 and the parabola y=x^2 about the following lines: a) the line x=6 b) the line x=-1 c)the x axis d) the line y=36 Thanks!
9. ### calculus 2

Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.
10. ### calculus 2

Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.

More Similar Questions