As traffic passes a sensor, the rate $N$ in cars per minute is measured at times in minutes: $N(0)=6$, $N(2)=9$, $N(7)=13$, $N(11)=18$. Use trapezoids on the three subintervals the table gives to approximate the total, in cars.

As a machine consumes power, the rate $P$ in kilowatts is measured at times in hours: $P(0)=5$, $P(2)=8$, $P(7)=12$, $P(11)=17$. Use trapezoids on the three subintervals the table gives to approximate the total, in kilowatt-hours.

As a colony grows, the rate $B$ in bacteria per hour is measured at times in hours: $B(0)=2$, $B(3)=5$, $B(8)=9$, $B(12)=14$. Use trapezoids on the three subintervals the table gives to approximate the total, in bacteria.

Approximate ${\int }_1^{3}2x^{2}dx$ with the TRAPEZOIDAL rule using $2$ equal subintervals.

As a colony grows, the rate $B$ in bacteria per hour is measured at times in hours: $B(0)=3$, $B(3)=6$, $B(6)=10$, $B(10)=15$. Use trapezoids on the three subintervals the table gives to approximate the total, in bacteria.

Which expression is the trapezoidal approximation of ${\int }_a^{b}f(x)dx$ with $3$ equal subintervals of width $4$?

A table gives $f(0)=3$, $f(3)=5$, $f(6)=7$, $f(9)=9$, $f(12)=11$, at inputs spaced $3$ apart. Use the trapezoidal rule to approximate ${\int }_0^{12}f(x)dx$.

For ${\int }_1^{5}2x^{2}dx$ with $2$ subintervals, the left sum is $40$ and the right sum is $136$. Without computing it, where does the trapezoidal sum $T$ fall?

For ${\int }_3^{6}3x^{2}dx$ with $3$ subintervals, the left sum is $150$ and the right sum is $231$. Without computing it, where does the trapezoidal sum $T$ fall?

Approximate ${\int }_1^{5}2x^{2}dx$ with the TRAPEZOIDAL rule using $2$ equal subintervals.

As water flows into a tank, the rate $R$ in gallons per minute is measured at times in minutes: $R(0)=6$, $R(3)=9$, $R(8)=13$, $R(12)=18$. Use trapezoids on the three subintervals the table gives to approximate the total, in gallons.

Approximate ${\int }_0^{4}4x^{2}dx$ with the TRAPEZOIDAL rule using $2$ equal subintervals.

Approximate ${\int }_2^6{x}^{2}dx$ with the TRAPEZOIDAL rule using $4$ equal subintervals.

Which expression is the trapezoidal approximation of ${\int }_a^{b}f(x)dx$ with $2$ equal subintervals of width $5$?

As a machine consumes power, the rate $P$ in kilowatts is measured at times in hours: $P(0)=6$, $P(2)=9$, $P(5)=13$, $P(9)=18$. Use trapezoids on the three subintervals the table gives to approximate the total, in kilowatt-hours.

Which expression is the trapezoidal approximation of ${\int }_a^{b}f(x)dx$ with $2$ equal subintervals of width $2$?

Approximate ${\int }_0^{4}2x^{2}dx$ with the TRAPEZOIDAL rule using $4$ equal subintervals.

A table gives $f(0)=1$, $f(3)=3$, $f(6)=5$, at inputs spaced $3$ apart. Use the trapezoidal rule to approximate ${\int }_0^{6}f(x)dx$.

As a machine consumes power, the rate $P$ in kilowatts is measured at times in hours: $P(0)=2$, $P(2)=5$, $P(5)=9$, $P(9)=14$. Use trapezoids on the three subintervals the table gives to approximate the total, in kilowatt-hours.

A table gives $f(0)=3$, $f(5)=5$, $f(10)=7$, $f(15)=9$, at inputs spaced $5$ apart. Use the trapezoidal rule to approximate ${\int }_0^{15}f(x)dx$.

For ${\int }_2^{6}3x^{2}dx$ with $2$ subintervals, the left sum is $120$ and the right sum is $312$. Without computing it, where does the trapezoidal sum $T$ fall?

Which expression is the trapezoidal approximation of ${\int }_a^{b}f(x)dx$ with $3$ equal subintervals of width $5$?

A table gives $f(0)=3$, $f(3)=5$, $f(6)=7$, at inputs spaced $3$ apart. Use the trapezoidal rule to approximate ${\int }_0^{6}f(x)dx$.

Approximate ${\int }_2^6{x}^{2}dx$ with the TRAPEZOIDAL rule using $2$ equal subintervals.