Use improper integration please find 24 to infinity.
Transcribed Image Text:The image shows a mathematical expression representing an improper integral. The integral is written as:
\[
\int_{24}^{\infty} A t^3 e^{-0.4t} \, dt
\]
This integral calculates the area under the curve of the function \( A t^3 e^{-0.4t} \) from \( t = 24 \) to infinity. In this context:
- \( A \) is a constant factor.
- \( t^3 \) denotes the cubic function of the variable \( t \).
- \( e^{-0.4t} \) is an exponential decay function, where \( e \) is the base of the natural logarithm.
- The limits of integration are from 24 to infinity, indicating that this is an improper integral because it extends indefinitely.
This kind of integral is often evaluated in contexts where exponential decay is an underlying factor, such as in physics or engineering applications involving decay processes or damping.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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![The image shows a mathematical expression representing an improper integral. The integral is written as:
\[
\int_{24}^{\infty} A t^3 e^{-0.4t} \, dt
\]
This integral calculates the area under the curve of the function \( A t^3 e^{-0.4t} \) from \( t = 24 \) to infinity. In this context:
- \( A \) is a constant factor.
- \( t^3 \) denotes the cubic function of the variable \( t \).
- \( e^{-0.4t} \) is an exponential decay function, where \( e \) is the base of the natural logarithm.
- The limits of integration are from 24 to infinity, indicating that this is an improper integral because it extends indefinitely.
This kind of integral is often evaluated in contexts where exponential decay is an underlying factor, such as in physics or engineering applications involving decay processes or damping.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbad65e5-4dc9-46c4-9488-acfd536277cd%2Fef3f2441-da64-4c19-89b2-3b23f82f2445%2Fwnfups_processed.jpeg&w=3840&q=75)
