SOLUTION: Calculate the following areas. First draw a neat sketch indicating the required area. Also show the area element (triangle A) 1. The area enclosed by the x-axis and that part of t

Algebra ->  Graphs -> SOLUTION: Calculate the following areas. First draw a neat sketch indicating the required area. Also show the area element (triangle A) 1. The area enclosed by the x-axis and that part of t      Log On


   

Question 1060302: Calculate the following areas. First draw a neat sketch indicating the required area. Also show the area element (triangle A)
1. The area enclosed by the x-axis and that part of the curve y=5x+6-x^2 for which y is positive.
2. The area enclosed by y=2 Sin 2x, the x-axis, x=0 and x=pi/2
3. The area enclosed by y=2e^2x, the x-axis, x=0 and x=2
Please assist!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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1.A=int%28%28-x%5E2%2B5x%2B6%29%2Cdx%2Cx=-1%2C6%29
A=-x%5E3%2F3%2B%285%2F2%29x%5E2%2B6x%2BC
A=-%286%5E3-%28-1%29%5E2%29%2F3%2B%285%2F2%29%286%5E2-%28-1%29%5E2%29%2B6%286-%28-1%29%29
A=-%28216%2B1%29%2F3%2B%285%2F2%29%2836-1%29%2B6%287%29
A=-%28217%29%2F3%2B%28175%2F2%29%2B42
A=%28-434%2B525%2B252%29%2F6
A=343%2F6
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2.A=int%28%282sin%282x%29%29%2Cdx%2Cx=0%2Cpi%2F2%29
A=-cos%282x%29%2BC
A=-cos%28pi%29%2Bcos%280%29
A=1%2B1%29
A=2
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3.A=int%28%282e%5E%282x%29%29%2Cdx%2Cx=0%2C2%29
A=e%5E%282x%29%2BC
A=e%5E%282%282%29%29-e%5E%282%280%29%29
A=e%5E4-1