Sums and Differences - Help (1 Viewer)

[laurajm]

hey can anyone help me?
please answer the questions step by step
1. find the area enclosed between the curves y=x^2 and y = x^3
2. find the area enclosed by the curves y = x^2 and x = y^2
3. find the area bounded by the curve y = x^2 + 2x - 8 and the line y = 2x+1
4. find the area bounded by the curves y = 1 - x^2 and y = x^2 - 1
5. find the exact area enclosed between the curve y = squareroot (4-x^2) and the line x - y + 2 = 0
thanks

 

[pLuvia]

For each question, do a rough sketch of each curve then determine which is the higher curve, then find where they intersect (those values will be your limits) then:
integration of the higher curve minus integration of the lower curve=answer

 

[laurajm]

yeah, i know that, but could u show me how to do them step by step. i have been doing this exercise for hours and i am struggling... please...

 

[watatank]

hey can anyone help me?
please answer the questions step by step
1. find the area enclosed between the curves y=x^2 and y = x^3
2. find the area enclosed by the curves y = x^2 and x = y^2
3. find the area bounded by the curve y = x^2 + 2x - 8 and the line y = 2x+1
4. find the area bounded by the curves y = 1 - x^2 and y = x^2 - 1
5. find the exact area enclosed between the curve y = squareroot (4-x^2) and the line x - y + 2 = 0
thanks

il walk you through the first question.

the formula needed is the integral of [ y₂ - y₁ dx]

if you graph the two you will find x² is the higher curve. so y₂ = x² and y₁ = x³. to find the limits its basically where they cross over. you can do simultaneous equations to find it. they cross over at x = 0,1 so thats your limits.

so its just the integral of [x² - x³] from a = 0 to b = 1. you can do the rest.

:wave:

 

[laurajm]

thnks