Check the solution to "Evaluate the integral. ∫e(42−44t)dt"

vakirnarhh

Answered question

2021-11-21

Evaluate the integral.

\int e^{(42 - 44 t)} d t

Stephanie Mann

Beginner2021-11-22Added 25 answers

Step 1
Consider the integral:

\int e^{(42 - 44 t)} d t

Suppose
u=42-44t
du=-44dt

d t = - \frac{1}{44} d u

Step 2
Substitute value in integrals then

\int e^{(42 - 44 t)} d t = \int e^{u} (- \frac{1}{44} d u)

= - \frac{1}{44} \int e^{u} d u

= - \frac{1}{44} e^{u} + C

\int e^{(42 - 44 t)} d t = - \frac{1}{44} e^{(42 - 44 t)} + C ∵ u = 42 - 44 t

Beulah Bryan

Beginner2021-11-23Added 4 answers

Step 1: Use Integration by Substitution.
Let u=42-44t, du=-44 dt, then

d t = - \frac{1}{44} d u

Step 2: Using u and du above, rewrite

\int e^{42 - 44 t} d t

\int - \frac{e^{u}}{44} d u

Step 3: Use Constant Factor Rule:

\int c f (x) d x = c \int f (x) d x

- \frac{1}{44} \int e^{u} d u

Step 4: The integral of

e^{x} i s e^{x}

- \frac{e^{u}}{44}

Step 5: Substitute tu=42−44t back into the original integral.

- \frac{e^{42 - 44 t}}{44}

Step 6: Add constant.

- \frac{e^{42 - 44 t}}{44} + C

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