91Ó°ÊÓ

In Exercises \(23-26\) use a calculator program to find the Simpson's Rule approximations with \(n=50\) and \(n=100 .\) $$\int_{0}^{1} \sqrt{1+x^{4}} d x$$

In Exercises \(23-28,\) use areas to evaluate the integral. $$\int_{0}^{b} 4 x d x, \quad b>0$$

In Exercises \(21-26,\) construct a function of the form \(y=\int^{x} f(t) d t+C\) that satisfies the given conditions. $$\frac{d y}{d x}=\sqrt{3-\cos x},\( and \)y=4\( when \)x=-3$$

In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { - 1 } ^ { 2 } 3 x ^ { 2 } d x$$

In Exercises \(21-26,\) construct a function of the form \(y=\int^{x} f(t) d t+C\) that satisfies the given conditions. $$\frac{d y}{d x}=\cos ^{2} 5 x,\( and \)y=-2\( when \)x=7$$

In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { - 2 } ^ { 6 } 5 d x$$

In Exercises \(23-26\) use a calculator program to find the Simpson's Rule approximations with \(n=50\) and \(n=100 .\) $$\int_{0}^{\pi / 2} \frac{\sin x}{x} d x$$

In Exercises \(23-28,\) use areas to evaluate the integral. $$\int_{a}^{b} 2 s d s, \quad 0 < a < b$$

In Exercises \(21-26,\) construct a function of the form \(y=\int^{x} f(t) d t+C\) that satisfies the given conditions. $$\frac{d y}{d x}=e^{\sqrt{x}},\( and \)y=1\( when \)x=0$$

In Exercises \(23-26\) use a calculator program to find the Simpson's Rule approximations with \(n=50\) and \(n=100 .\) $$\int_{0}^{\pi / 2} \sin \left(x^{2}\right) d x$$