Chapter 26

Find the area (in square units) bounded by each curve, the given lines, and the \(x\) axis. Sketch the curve for some of these, and try to make a quick estimate of the area. Also check some graphically or by calculator. \(y=2 x\) from \(x=0\) to 10

Solve each differential equation.$$\frac{d y}{d x}=4 x^{2}$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{1}^{2} x d x$$

Evaluate each integral. Check some by calculator. $$\int\left(x^{4}+1\right)^{3} 4 x^{3} d x$$

Find each indefinite integral. Check some by calculator. $$\int d x$$

Solve each differential equation.$$\frac{d y}{d x}=2 x\left(x^{2}+6\right)$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{-2}^{2} x^{2} d x$$

Evaluate each integral. Check some by calculator. $$\int\left(2 x^{2}-6\right)^{3} 4 x d x$$

Find each indefinite integral. Check some by calculator. $$\int d y$$

Find the area (in square units) bounded by each curve, the given lines, and the \(x\) axis. Sketch the curve for some of these, and try to make a quick estimate of the area. Also check some graphically or by calculator. \(y=3+x^{2}\) from \(x=-5\) to 5

Solve each differential equation.$$\frac{d y}{d x}=x^{-3}$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{1}^{3} 7 x^{2} d x$$

Evaluate each integral. Check some by calculator. $$\int 9\left(x^{3}+1\right)^{2} x^{2} d x$$

Find each indefinite integral. Check some by calculator. $$\int 6 \, d x$$

Solve each differential equation.$$\frac{d s}{d t}=10 t^{-6}$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{-2}^{2} 3 x^{4} d x$$

Evaluate each integral. Check some by calculator. $$\int 6\left(x^{2}-1\right)^{2} x d x$$

Find each indefinite integral. Check some by calculator. $$\int-2 \, d x$$

Find the area (in square units) bounded by each curve, the given lines, and the \(x\) axis. Sketch the curve for some of these, and try to make a quick estimate of the area. Also check some graphically or by calculator. \(y=x^{3}\) from \(x=0\) to 4

Solve each differential equation.$$\frac{d s}{d t}=\frac{1}{2} t^{-2 / 3}$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{0}^{4}\left(x^{2}+2 x\right) d x$$

Evaluate each integral. Check some by calculator. $$\int 2\left(x^{2}+2 x\right)^{3}(2 x+2) d x$$

Find each indefinite integral. Check some by calculator. $$\int 5 \, d x$$

Find the area (in square units) bounded by each curve, the given lines, and the \(x\) axis. Sketch the curve for some of these, and try to make a quick estimate of the area. Also check some graphically or by calculator. \(y=9-x^{2}\) from \(x=0\) to 3

Solve each differential equation.$$\frac{d v}{d t}=6 t^{3}-3 t^{-2}$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{-2}^{2} x^{2}(x+2) d x$$

Evaluate each integral. Check some by calculator. $$\int(x+1)\left(x^{2}+2 x+6\right)^{2} d x$$

Find each indefinite integral. Check some by calculator. $$\int 7 \, d y$$

Find the area (in square units) bounded by each curve, the given lines, and the \(x\) axis. Sketch the curve for some of these, and try to make a quick estimate of the area. Also check some graphically or by calculator. \(y=1 / \sqrt{x}\) from \(x=\frac{1}{2}\) to 8

Solve each differential equation, including evaluation of the constant of integration.$$y^{\prime}=3 x, \text { passes through }(2,6)$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{2}^{4}(x+3)^{2} d x$$

Evaluate each integral. Check some by calculator. $$\int \frac{d x}{(1-x)^{2}}$$

Find each indefinite integral. Check some by calculator. $$\int \pi d x$$

Graph region. Make a quick estimate of the indicated area, and then use a graphical method to find its approximate value. $$y=x^{2}+3 \quad \text { from } x=-4 \text { to } 4$$

Solve each differential equation, including evaluation of the constant of integration.$$y^{\prime}=x^{2}, \text { passes through }(1,1)$$

Evaluate each integral. Check some by calculator. $$\int \frac{4 x d x}{\left(9-x^{2}\right)^{2}}$$

Find each indefinite integral. Check some by calculator. $$\int 42 \, d x$$

Find the area (in square units) bounded by each curve, the given lines, and the \(x\) axis. Sketch the curve for some of these, and try to make a quick estimate of the area. Also check some graphically or by calculator. \(y=x^{2}+x+1\) from \(x=2\) to 3

Solve each differential equation, including evaluation of the constant of integration.$$y^{\prime}=\sqrt{x}, \text { passes through }(2,4)$$

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{1}^{10} \frac{d x}{x}$$

Evaluate each integral. Check some by calculator. $$\int x \sqrt{x^{2}-2} d x$$

Find each indefinite integral. Check some by calculator. $$\int x \, d x$$

Find the area (in square units) bounded by each curve, the given lines, and the \(x\) axis. Sketch the curve for some of these, and try to make a quick estimate of the area. Also check some graphically or by calculator. \(y=\sqrt{3 x}\) from \(x=2\) to 8

Solve each differential equation, including evaluation of the constant of integration.If \(d y / d x=2 x+1,\) and \(y=7\) when \(x=1,\) find the value of \(y\) when \(x=3\).

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{1}^{e} \frac{d x}{x}$$

Evaluate each integral. Check some by calculator. $$\int 3 x \sqrt{x^{2}-1} d x$$

Find each indefinite integral. Check some by calculator. $$\int x^{2} d x$$

Evaluate expression. $$\sum_{n=1}^{5} n$$

Solve each differential equation, including evaluation of the constant of integration.If \(d y / d x=\sqrt{2 x},\) and \(y=\frac{1}{3}\) when \(x=\frac{1}{2},\) find the value of \(y\) when \(x=2\).

Evaluate each definite integral to three significant digits. Check some by calculator. $$\int_{0}^{1} \frac{x d x}{\sqrt{4+x^{2}}}$$