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

2) Suppose . Evaluate the following integrals.

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

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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