The region bounded by the x axis, the y axis, the line y = 2 and the parabola y? = 12 – 4x is revolved about the x axis. Find the volume of solid generated.

Q: Add or subtract terms whenever possible. 8√5 + 11√5

A:

Q: The graph of the function f consists of the three line segments joining the points (0, 0), (2, −2), ...

A: (a) Plot the points on the graph and join the line segments to construct the graph of f(x).

Q: To evaluate the integral | x sin(x2) dx we use the substitution O a. x= t O b. sinx =t O c. sin x2 =...

A: Explanation of the solution is given below....

Q: Find parametric equations for the lines in The line through P(1, 2, -1) and Q(-1, 0, 1)

A:

Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to des...

A: Projection of vector u onto v will be: Projvu=u→·v→v→ Therefore, Projection of vector u onto v is gi...

Q: Calculate the iterated integral

A: Definition used-    Double integral -                             ∫ab∫cdg(y)f(x)dxdy                ...

Q: Find a formula for the distance from the point P(x, y, z) to thea. xy-plane. b. yz-plane. c. xz-plan...

A: Distance FormulaDistance between two points x1,y1,z1 and x2,y2,z2d=x2−x12+y2−y12+z2−z12

Q: Evaluate x*zdx – yx dy + 6 dz along C the curve C shown in the figure. A Z 2 2 y 2 x.

A: By making it in to three sub curves we integrate and add the results then we will ge the answers 

Q: Solve the logarithmic equation ln√(x + 4) = 1. Be sure to reject any value of x that is not in the d...

A: The given logarithmic equation is: lnx+4=1 To solve this equation, first, take the antilogarithmic o...

Q: | cos(x) sin(2x) dæ

A:

Q: Graphing curves Graph the curves described by the following functions, indicating the positive orien...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Multiply or divide. [(x2 + x - 12/x2 + x - 30) . (x2 + 5x + 6/x2 - 2x - 3)÷(x + 3/x2 + 7x + 6)]

A: x2+x-12x2+x-30·x2+5x+6x2-2x-3÷x+3x2+7x+6⇒x4+x3-12+x3-30x2x2·x4+5x3+6-2x3-3x2x2÷x3+3+7x3+6x2x2⇒x4+2x3...

Q: Evaluate using Partial fraction method S X-7 Jx+ 4)(x² + 9) ° xp-

A:

Q: Find the exact value of the expression cos 11π/6. Do not use a calculator.

A: To find the exact value of the expression,cos11π6. Solution: The given expression is , cos11π6 Simpl...

Q: Evaluate the integral.  integral cos  - 6  x  dx

A: To evaluate the integral, ∫cos-6xdx Solution: The given integral can be written as, ∫1cos6xdx=∫sec6x...

Q: Volume of a solid Consider the region R bounded by the graph of f(x) and the x-axis on the interval ...

A: Volume of solid: Let f(y) and g(y) are two curves then volume of the solid around y axis is, V=2π∫ab...

Q: Solve the initial value problems d2y/dx2 = 2 - 6x; y'(0) = 4, y(0) = 1

A: We have to solve the initial value problem: d2ydx2=2-6x; y'0=4,  y0=1 Integrating both sides, ∫d2ydx...

Q: In each part, find all values of x for which the series con- verges, and find the sum of the series ...

A: Given, e-x+e-2x+e-3x+e-4x+e-5x+..

Q: Determine the convergence or divergence of the sequence with the given nth term an = n/ln n. If the ...

A:  

Q: Polar to Cartesian coordinates Convert the polar equation r = 10 cos θ + 24 sin θ to Cartesian coord...

A: Given polar equation is r=10cosθ+24sinθ. We know that in rectangular coordinates, we have x=rcosθ, y...

Q: Approximate the change in the volume of a right circular cylinderof fixed radius r = 20 cm when its ...

A: Approximate the change in the volume of a right circular cylinder of fixed radius r = 20 cm when its...

Q: Write equations in point-slope form, slope-intercept form, and general form for the line passing thr...

A: y=-14x+13 Comparing with y=mx+c, we get m=slope=-14 Therefore slope of required line is, -1-14=4   ∵...

Q: Q. If u = x³tan-1 then x au - +y ay ax au is а. u b. 0 С. 2u d. 3u

A:

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A: limθ→0+sinθtanθ

Q: Suppose that g(x) is an unknown function such that g(V3) = -2 and g' (V3) = 8. Now suppose we define...

A: Given that g3=-2  and  g'3=8. Consider the function fx=tan-1xgx. This implies that, fx=tan-1xgxlnfx=...

Q: In Simpson's method , h=0.25, b=5, N=4 then the value of a= a. 3 b. 4 c. 2 d. 8

A: Consider the following variables, a=lower limitb=upper limitn=number of sub-intervalsh=length of eac...

Q: Determine the validity interval for solving the initial value problem

A: Solution: The objective is to find the solution of the given differential equation

Q: Fill in the blank : We simplify a rational expression by ..............the numerator and the denomin...

A: To simplify a rational expression first we  factor the numerator and denominator completely. Then we...

Q: Question (1)  Prove , ez1/ez2  = ez1-z2

A: The given equation is: ez1ez2=ez1-z2

Q: Explain the Chain Rule for two independent Variables ?

A: Chain rule for two independent variables: Let x=gu,v and y=hu,v be two differentaibel function of u ...

Q: In Exercises 1–8, find the length and direction (when defined) of u * v and v * u.

A: The vectors are: u = 2i - 2j - k v = i - k Then we get,  

Q: x³ In x dx

A:

Q: The value of the integral e-X dx is O a. 0 b. 00 О с. 1 O d. -1

A:

Q: Problem - 1: Find the interval of convergence of the series 1 (x-3)+-(x-3)² + (x-3)" +…….. …….+

A:

Q: (a) Find a continuous solution satisfying the differential equation and the given initial condition.

A: The given problem is an initial value problem:   Since,             We need to find the continuous s...

Q: What are eigenvalues ?

A: What are eigenvalues ?

Q: Find the work done by the force field F(x, y) = xyi+ x²j on a ,2 particle that moves along the curve...

A: Consider the given force field Fx,y=xyi+x2j Then, F⇀x,y=xy,y Write in parametric form y=t  then  x=t...

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.