Chapter 6.2, Problem 58E

Decide whether you can find each integral using the formulas and techniques you have studied so far. Explain. (a) ∫2dx / √(x2 + 4)        (b) ∫dx/x√(x2 − 9)

What have you learned in evaluating integrals?

What is the area of the auxiliary rectangle of x^2/4-y^2/9=1

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.

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)

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

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.