Reference no: EM13990608

1) Make the appropriate substitutions in the following integrals without evaluating the integrals.

(a) ∫x³√(x²+2) dx

(b) ∫(x²/(√1-x²)) dx

(c) ∫(x²/x²+2x+2) dx

2) Consider ∫(x/√(x²-2)) dx

(a) Which is the most appropriate technique to evaluate this integral?

(b) Use the indicated technique to evaluate this integral.

(c) Evaluate this integral using a different technique.

3) Evaluate the following integrals using integration by parts.

(a) ∫e^xsinx dx

(b) ₀∫^πx²cos(2x) dx

(c) ∫x√(x+2) dx

4) Evaluate the following limits:

(a) lim_x→0 sinx/e^x-1

(b) kim_x→0+ sin(x²)/x²

5) Strontium -90 has a half-life of 28 days. Find a formula that gives the amount of strontium left after time t if you start one 200 grams. How long does it take for 80% of the Strontium to decay.