Question
During a thunderstorm, rain was falling at the rate of$$8 \sqrt{2 t}-32 t^{3} \quad(0 \leq t \leq 0.6)$$ in. /hr.a. Find an expression giving the total amount of rainfall after $t$ hr.b. How much rain had fallen after $\frac{1}{2} \mathrm{hr} ?$
Step 1
To find the total amount of rainfall after $t$ hours, we need to integrate this rate function with respect to $t$. Show more…
Show all steps
Your feedback will help us improve your experience
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
During a thunderstorm, rain was falling at the rate of $$8 \sqrt{2 t}-32 t^{3} \quad(0 \leq t \leq 0.6)$$ in./hr. a. Find an expression giving the total amount of rainfall after $t$ hr. Hint: The total amount of rainfall at $t=0$ is zero. b. How much rain had fallen after $\frac{1}{2} \mathrm{hr}$ ?
Integration
Antiderivatives and the Rules of Integration
The rates at which rain fell, in inches per hour, in two different locations $t$ hours after the start of a storm were modeled by $f(t)=0.73 t^{3}-2 t^{2}+t+0.6$ and $g(t)=0.17 t^{2}-0.5 t+1.1 .$ Compute the area between the graphs for $0 \leqslant t \leqslant 2$ and interpret your result in this context.
Applications of Integration
Areas Between Curves
The rates at which rain fell, in inches per hour, in two different locations $t$ hours after the start of a storm were modeled by $f(t)=0.73 t^{3}-2 t^{2}+t+0.6$ and $g(t)=0.17 t^{2}-0.5 t+1.1$. Compute the area between the graphs for $0 \leqslant t \leqslant 2$ and interpret your result in this context.
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD