Problems

In Problems 1-90, evaluate the integral.

In Problems 91-108, evaluate the definite integral.

109          Find the area of the region below the curve y = 1/(10 - 3x) from x = 1 to x = 2.

110          Find the area of the region under one arch of the curve y = sin x cos x.

111          Find the area of the region under one arch of the curve y = cos (3x).

112          Find the area of the region below the curve between x = 0 and x = 2.

113          Find the area below the curve y = (1 + 7x)^2/3 between x = 0 and x = 1.

114          Find the area below the curve y = x/(x² + 1)² between x = 0 and x = 3.

117          Let f and g have continuous derivatives and evaluate f'(g(x))g'(x) dx.

118          A real function f is said to be even if f (x) = f (- x) for all x. Show that if f is a continuous even function, then

119          An odd function is a real function g such that g(-x) = -g(x) for all x. Prove that for a continuous odd function g,