A laboratory heater operates according to the schedule below: • : power is constant at

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A laboratory heater operates according to the schedule below: •

0\,\text{s}\le t<5\,\text{s}

: power is constant at

80\,\text{W}

. •

5\,\text{s}\le t<10\,\text{s}

: power increases linearly from

80\,\text{W}

t=5\,\text{s}

200\,\text{W}

t=10\,\text{s}

. •

10\,\text{s}\le t\le14\,\text{s}

: power is constant at

50\,\text{W}

. Determine the total energy transferred to the heater’s surroundings over the entire

14\,\text{s}

period.