SOLUTION: The power (in Watts) from an engine is represented by the equation : P = 100t^1.4 + 6t , where t is the time.? in Seconds. 1: Draw the graph that represents power against time

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Question 1028629: The power (in Watts) from an engine is represented by the equation : P = 100t^1.4 + 6t , where t is the time.?
in Seconds.
1: Draw the graph that represents power against time for this engine.
2.show the area on the graph which represents the energy converted between 5s and 15s
3. show, using summation how you would gain an approximation for the energy
4. using intergration, evaluate the exact energy between 5s and 15s
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1. .
2. Area of the trapezoid marked by the black dashed boundaries and the graph.
3. You could just calculate the area of the trapezoid or using a dx, make a summation.
A=sum%28P%28x%29%2Adx%2Cx=1%2CN%29
4. int%28P%28t%29%2Cdt%2C5%2C15%29=100%28t%5E%281.4%2B1%29%29%2F%282.4%29%2B3t%5E2%2BC

int%28P%28t%29%2Cdt%2C5%2C15%29=%28125%2F3%29%28664.69-47.59%29%2B3%28225-25%29
int%28P%28t%29%2Cdt%2C5%2C15%29=%28125%2F3%29%28617.1%29%2B3%28200%29
int%28P%28t%29%2Cdt%2C5%2C15%29=25712.5%2B600
int%28P%28t%29%2Cdt%2C5%2C15%29=26312.5Watt-sor J
As a comparison, the area of the trapezoid would yield,
A=%281%2F2%29%2810%29%284431.265%2B951.827%29
A=27515.5
Also, a summation using dx=0.5 would yield,
A=27061.3
Even closer.