Chapter 6.2, Problem 60E

Explain how to evaluate a definite integral using area -what area should be shaded -where the area is relative to the x-axis -what shapes could be involved -what could make the value of an integral equal a negative value -what could make the value of an integral equal to zero  -what is the order of the endpoints on the integral and what happens if they are reversed.

Give an example showing how to use rectangles to estimate the area under a curve.  Then use integration to find the exact area under the same curve.

integrate x ^ 3 * sqrt(x ^ 2 + 3) dx from 0 to 1. Kindly evaluate the definite integral and write complete solutions. Thank you

a circular city has a density of population equal to 500/(1+r) where r is the radius, write an integral expression for the number of people who live within 10 miles of the city

Hi what is the integral of x^2

Evaluate the integral sec(theta)/sec(theta)-tan(theta) d(theta) A. sec2(theta) - tan(theta) + CB. tan(theta) + sec(theta) + CC. tan2(theta) + sec(theta) + C D. tan (theta) - sec(theta) +C please let me know if you need a picture. I wish i was able to format the integral better here.  sec(x)/sec(x)-tan(x) dx (this is to help if you don't understand the theta input)

please show steps so i can understand, i got a very long answer and dont think its correct