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1) Use the limit definition of the definite integral with right Riemann sums to evaluate the following definite integral.

LaTeX: int^1_0left(4x-2right)dx

2) Suppose LaTeX: int^4_1fleft(xright)dx=6,::int^4_1gleft(xright)dx=4,::and:int^4_3fleft(xright)dx=2. Evaluate the following integrals.

a) LaTeX: int^4_1left(3fleft(xright)-2gleft(xright)right)dx

b) LaTeX: int^3_1fleft(xright)dx

3) Evaluate the following derivative. LaTeX: frac{d}{dx}int^{e^{2x}}_3cosleft(t^2right)dt:

4) Evaluate the following integrals.

a) LaTeX: int^2_{-2}left(3x^4-2x+1right)dx

b) LaTeX: int^{frac{pi}{3}}_{frac{pi}{6}}left(sec^2t+csc^2tright)dt:

c) LaTeX: intcosleft(3xright)dx

d) LaTeX: int^5_{-5}frac{w^3}{sqrt[]{w^{50}+w^{20}+1}}dw::left[Hint.::Use:Symmetryright]


e) LaTeX: int^1_0frac{v^3+1}{sqrt[]{v^4+4v+4}}dv

f) LaTeX: int e^{sin^2x}sin2xdx::left[Hint.::sin2x=2sin xcosxright]:

5) Find the average value of the following function on the given interval. LaTeX: fleft(xright)=frac{1}{x}:on:left[1,eright]

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