Evaluate the definite integrals

Assignment Help Mathematics

Reference no: EM133518810

Question # 1

Use the definition of improper integral (by using lim_b→∞ _x=∫^b...dx) to evaluate the following

A) _e∫^∞5/(x(lnx)²).dx =

B) ₀∫²(3x²)/√(8-x³ ).dx =

Question # 2 Evaluate the following definite integrals. Clearly state { u = du= ,v= ,dv= }, when appropriate

(A) 5₀∫^π xcos(x/2).dx =

(B) ₁∫² x² e^-5x dx =

Question # 3 Evaluate each integral. (Clearly state substitution, when appropriate)

A) ∫cos(5x)/(1+sin(5x)).dx =

B) ∫cos(√x)/√x dx =

C) ∫sec²(x)/(5+tan(x)) dx =

D) ₀∫³ 2x/√(5 + x²).dx =

E) ₁∫^e √(ln(x))/x dx =

Question # 4 Evaluate the first integral as a sum of two integrals. (Clearly state substitution when appropriate).

∫(4x+11)/(x²+4x+5) dx = ∫(4x+8)/(x²+4x+5) dx+∫3/(x²+4x+5) dx

In this section, when appropriate, you can apply:

∫ 1/(a² + x²) dx = 1/a arctan(x/a) + C

Reference no: EM133518810

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