How do you evaluate #int 1/750* (x+10)^4 *e^(-.07) # for [0,125]?

Question

Emilia Aguilar · Accepted Answer

Remove any constants from the integrand, then integrate.

#int_0^125(1/750)(x+10)^4e^-0.07dx# #=(1/750)(e^-0.07)int_0^125(x+10)^4dx# Now, integrate the polynomial with respect to x: #=(1/750)(e^-0.07)(x+10)^5/5# Finally, evaluate at the upper and lower limits [0,125] #=[(1/750)(e^-0.07)(125+10)^5/5]# - #[(1/750)(e^-0.07)(0+10)^5/5]# #= 11,149,002 Hope that helped

Cameron Alexander · Answer

undefined To evaluate the expression $ \frac{1}{750} (x+10)^4 e^{-0.07} $ over the interval [0,125], you would:

1. Substitute the upper limit of the interval, $ x = 125 $, into the expression.
2. Substitute the lower limit of the interval, $ x = 0 $, into the expression.
3. Calculate the difference between the two results obtained from steps 1 and 2.

Axel Alvarez · Answer

undefined To evaluate the integral $\int \frac{1}{750} (x+10)^4 e^{-0.07} \, dx$ over the interval [0, 125], you can follow these steps:

1. First, distribute the constants and rewrite the integral:
   $\frac{1}{750} e^{-0.07} \int (x+10)^4 \, dx$

2. Integrate the expression $(x+10)^4$:
   $\int (x+10)^4 \, dx = \frac{1}{5}(x+10)^5 + C$

3. Apply the limits of integration [0, 125]:
   $\frac{1}{5} [(125+10)^5 - (0+10)^5]$

4. Substitute the values and calculate the result:
   $\frac{1}{5} [(135)^5 - (10)^5]$

5. Finally, simplify the expression to find the numerical value of the integral over the given interval.

This process will yield the numerical value of the integral over the interval [0, 125].