1.7.2 Integration

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Question 52

The rate of change of the volume of liquid, $V\,$ in $cm3\text{cm}^3$ , in a hydraulic cylinder is modeled by the derivative $dVdt=10t4−23t5+34\displaystyle \frac{dV}{dt} = 10t^4 - \frac{2}{3t^5} + \frac{3}{4}$ for $t > 0$ , where $t\,$ is the time in seconds. Find the general expression for $V\,$ by evaluating:

\int \left( 10t^4 - \frac{2}{3t^5} + \frac{3}{4} \right) dt

giving each term in its simplest form.

[4]

1.7.2 Integration

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Question 52

The rate of change of the volume of liquid, $V\,$ in $cm3\text{cm}^3$ , in a hydraulic cylinder is modeled by the derivative $dVdt=10t4−23t5+34\displaystyle \frac{dV}{dt} = 10t^4 - \frac{2}{3t^5} + \frac{3}{4}$ for $t > 0$ , where $t\,$ is the time in seconds. Find the general expression for $V\,$ by evaluating:

\int \left( 10t^4 - \frac{2}{3t^5} + \frac{3}{4} \right) dt

giving each term in its simplest form.

[4]

1.7.2 Integration

Question 52

1.7.2 Integration Questions

1.7.2 Integration

Question 52

1.7.2 Integration Questions