# Get integral calculus homework help # Recent questions in Integral Calculus

Differential equations
ANSWERED ### $$\displaystyle{y}'={\left({y}+{4}{x}\right)}^{{2}}$$

Decimals
ANSWERED ### Change the following decimals to fractions. Give each fraction in its simplest form. a) 4.2, b) 0.06, c) 1.85, d) 2.005.

Differential equations
ANSWERED ### $$\displaystyle{d}^{{2}}\frac{{y}}{{\left.{d}{x}\right.}^{{2}}}−{2}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}+{10}{y}={0}$$ where $$x=0;y=0$$ and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}?{x}={0};{y}={0}$$ and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}$$?

Differential equations
ANSWERED ### In many physical applications, the nonhomogeneous term F(x) is specified by different formulas in different intervals of x. (a) Find a general solution of the equation $$\displaystyle{y}{''}+{y}=\left\{{x},{0}\leq{x}\leq{1},{1}\leq{x}\right\}$$ NoteNote that the solution is not differentiable at x = 1. (b) Find a particular solution of $$y''+y=\left\{x,0\leq x\leq 1;1,1\leq x\right\}$$ that satises the initial conditions y(0)=0 and y′(0)=1.

Decimals
ANSWERED ### Change the following decimals to fractions. Give each fraction in its simplest form. a) 4.2, b) 0.06, c) 1.85, d) 2.005.

Differential equations
ANSWERED ### $$\displaystyle{2}⋅{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}+{2}{y}={0}$$

Decimals
ANSWERED ### Write the decimals in words. Write the money amounts in words for dollars and fractions for cents. Write the words in decimals. 0.4

Applications of integrals
ANSWERED ### Explain why each of the following integrals is improper. (a) $$\int_6^7 \frac{x}{x-6}dx$$ -Since the integral has an infinite interval of integration, it is a Type 1 improper integral. -Since the integral has an infinite discontinuity, it is a Type 2 improper integral. -The integral is a proper integral. (b)$$\int_0^{\infty} \frac{1}{1+x^3}dx$$ Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (c) $$\int_{-\infty}^{\infty}x^2 e^{-x^2}dx$$ -Since the integral has an infinite interval of integration, it is a Type 1 improper integral. -Since the integral has an infinite discontinuity, it is a Type 2 improper integral. -The integral is a proper integral. d)$$\int_0^{\frac{\pi}{4}} \cot x dx$$ -Since the integral has an infinite interval of integration, it is a Type 1 improper integral. -Since the integral has an infinite discontinuity, it is a Type 2 improper integral. -The integral is a proper integral.

Parametric equations, polar coordinates, and vector-valued functions
ANSWERED ### Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).

Integrals
ANSWERED ### Use a double integral to find the area of the region. The region inside the cardioid $$r=1+\cos \theta$$ and outside the circle $$r=3 \cos \theta$$

Differential equations
ANSWERED ### Which is a narrow, debatable claim?

Parametric equations, polar coordinates, and vector-valued functions
ANSWERED ### Use the table of values of $$f(x, y)$$ to estimate the values of $$fx(3, 2)$$, $$fx(3, 2.2)$$, and $$fxy(3, 2)$$. $$\begin{array}{|c|c|}\hline y & 1.8 & 2.0 & 2.2 \\ \hline x & & & \\ \hline 2.5 & 12.5 & 10.2 & 9.3 \\ \hline 3.0 & 18.1 & 17.5 & 15.9 \\ \hline 3.5 & 20.0 & 22.4 & 26.1 \\ \hline \end{array}$$

Parametric equations, polar coordinates, and vector-valued functions
ANSWERED ### Determine whether the given vectors are orthogonal, parallel,or neither: $$u=(-3,\ 9,\ 6)$$ $$v=(4,\ -12,\ -8)$$

Parametric equations, polar coordinates, and vector-valued functions
ANSWERED ### Change from rectangular to cylindrical coordinates. (Let $$r\geq0$$ and $$0\leq\theta\leq2\pi$$.) a) $$(-2, 2, 2)$$ b) $$(-9,9\sqrt{3,6})$$ c) Use cylindrical coordinates. Evaluate $$\int\int\int_{E}xdV$$ where E is enclosed by the planes $$z=0$$ and $$z=x+y+10$$ and by the cylinders $$x^{2}+y^{2}=16$$ and $$x^{2}+y^{2}=36$$ d) Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone $$z=\sqrt{x^{2}+y^{2}}$$ and the sphere $$x^{2}+y^{2}+z^{2}=8$$.

Decimals
ANSWERED ### Show that the decimals 0.6, 0.1, 0.2, and 0.325 are positive rational numbers.

Parametric equations, polar coordinates, and vector-valued functions
ANSWERED ### 1) Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant. 2) Use polar coordinates to find the volume of the given solid. Bounded by the paraboloid $$z = 5 + 2x^2 + 2y^2$$ and the plane z = 11 in the first octant

Differential equations
ANSWERED ### You have a $150 gift card to use at a sporting goods store. You buy 2 pairs of shoes for$65. You plan to spend the rest of the money on socks. Socks cost \$4.75 per pair. What is the greatest number of pairs of socks you can purchase?

Parametric equations, polar coordinates, and vector-valued functions
ANSWERED ### Express as a trigonometric function of one angle. a) $$\cos2\sin(-9)-\cos9\sin2$$ Find the exact value of the expression. b) $$\sin\left(\arcsin\frac{\sqrt{3}}{2}+\arccos0\right)$$

Integrals
ANSWERED ### Describe in words the surface whose equation is given. $$\phi = \frac{\pi}{4}$$ (select the correct answer) 1)the top half of the right circular cone with vertex at the origin and axis the positive z-axis 2)the plane perpendicular to the xz-plane passing through z = x, where $$x \geq 0$$ 3)the plane perpendicular to the xy-plane passing through y = x, where $$x \geq 0$$ 4)the base of the right circular cone with vertex at the origin and axis the positive z-axis 5)the plane perpendicular to the yz-plane passing through z = y, where $$y \geq 0$$
ANSWERED 