Which of these statements is true?
A) $ \int_{0}^{\infty} t^{-4} e^{4 t} d t $ converges because $ \frac{e^{4 t}}{t^{4}} \leq e^{4 t} $, for all $ t \geq 1 $ and $ \int_{0}^{\infty} e^{4 t} d t $ converges.
B) $ \int_{0}^{\infty} t^{2} e^{-5 t} d t $ diverges because $ t^{2} e^{-5 t} \geq t^{2} $, for all $ t \geq 1 $ and $ \int_{0}^{\infty} t^{2} d t $ converges.
C) $ \int_{0}^{\infty} A^{4} e^{-2 t} d t $ converges because $ t^{t} e^{-2 t} $ is of exponential order.
D) $ \int_{0}^{\infty} t^{-4} e^{2 t} d t $ converges because $ t^{-4} e^{2 t} $ is of exponential order.

Question

Quizplus · Accepted Answer

The Answer of Which of these statements is true?
A) $ \int_{0}^{\infty} t^{-4} e^{4 t} d t $ converges because $ \frac{e^{4 t}}{t^{4}} \leq e^{4 t} $, for all $ t \geq 1 $ and $ \int_{0}^{\infty} e^{4 t} d t $ converges.
B) $ \int_{0}^{\infty} t^{2} e^{-5 t} d t $ diverges because $ t^{2} e^{-5 t} \geq t^{2} $, for all $ t \geq 1 $ and $ \int_{0}^{\infty} t^{2} d t $ converges.
C) $ \int_{0}^{\infty} A^{4} e^{-2 t} d t $ converges because $ t^{t} e^{-2 t} $ is of exponential order.
D) $ \int_{0}^{\infty} t^{-4} e^{2 t} d t $ converges because $ t^{-4} e^{2 t} $ is of exponential order.

Which of These Statements Is True? A) ∫0∞t−4e4tdt \int_{0}^{\infty} t^{-4} e^{4 t} d t ∫0∞​t−4e4tdt

Which of These Statements Is True?
A) $\int_{0}^{\infty} t^{-4} e^{4 t} d t$