Multiple Choice 1 point If $f(t)$ is measured in $\frac{meters}{second^2}$ and $t$ is measured in seconds, what are the units of the $\int_a^b f(t) dt$? seconds meters/second$^3$ meters meters/second seconds/meter
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The unit of $t$ is $seconds$. The integral $\int_a^b f(t) dt$ represents the area under the curve of $f(t)$ from $a$ to $b$. The unit of the integral is the product of the unit of $f(t)$ and the unit of $t$. Show more…
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For the following problems, the units of a variable are given along with the units for a function (or two functions). Give the units of each definite integral. (a) If x is in "seconds" and f(x) is in "feet/second" then int_a^b f(x)dx is in feet/sec^2 feet/sec feet feet.sec (b) If t is in "seconds" and g(t) is in "feet/seconds^2" then int_a^b g(t)dt is in feet/sec^2 feet/sec feet feet.sec (c) If x is in "days" and f(x) is in "degrees F" then int_a^b f(x)dx is in days (degrees F)/day degrees F (degrees F).days (d) If x is in "hours" and g(x) is in "kilowatts" then int_a^b g(x)dx
Manisha S.
Daniel C.
(a) If $h^{\prime}(t)$ is the rate of change of a child's height measured in inches per year, what does the integral $\int_{0}^{10} h^{\prime}(t) d t$ represent, and what are its units? (b) If $r^{\prime}(t)$ is the rate of change of the radius of a spherical balloon measured in centimeters per second, what does the integral $\int_{1}^{2} r^{\prime}(t) d t$ represent, and what are its units? (c) If $H(t)$ is the rate of change of the speed of sound with respect to temperature measured in $\mathrm{ft} / \mathrm{s}$ per $^{\circ} \mathrm{F}$, what does the integral $\int_{32}^{100} H(t) d t$ represent, and what are its units? (d) If $v(t)$ is the velocity of a particle in rectilinear motion. measured in $\mathrm{cm} / \mathrm{h}$, what does the integral $\int_{t_{1}}^{t_{2}} v(t) d t$ represent, and what are its units?
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