Find the area of the region. See Examples 1, 2, 3, and 4. f(x) - x2 + 4x + 4 9(x) - 4x + 20 y 40 30 20 10 - 10 -5 5

Q: show all work

A: It is known that area of region bounded by the curves is given by the integral, A=∫abf2(x)-f1(x)dx  ...

Q: Suppose the position function for a free-falling object on a certain planet is given by s(1) =- 1412...

A: Given: st=-14t2+v0t+s0

Q: The variable c is inversely proportional to f. Write an equation that states this relationship. Assu...

A:

Q: Anti-differentiate using an appropriate technique ∫dx/x^2√1−x^2

A: In general, the integral of a real valued function f(x) with respect to a real variable x on an inte...

Q: Look at picture please!

A: Given,

Q: Find the volume of a parallelepiped if four of its eight vertices are A(0,0,0), B(1,3,0), C(0, – 4,3...

A: Given vertex of parallelepipedA0,0,0B1,3,0C0,-4,3D2,4,-5

Q: Solve the differential equation

A: We have to solve the given differential equation  xyy'=x2+1

Q: Use the table below to find (4g(x) + 2x] 3. 4 4. 3. f'(x) g'(x) 3 4 212

A: Derivative of the function decides whether the function is increasing or decreasing. If the first de...

Q: Consider the double integral dxdy. By converting to polar coordinates, the limits of integration of ...

A: Given, ∫032/2∫x=y9-y2dxdy where region is bounded by x=9-y2,  y=xx2+y2=9,    y=x now find intersecti...

Q: es AB3: Let h(x) = - Find h'(6). 3x %3D 3

A: Here we have,  h(x)=eg(x)3x ....................(1)  we have to find h'(6)=? Now differentiate equat...

Q: Using implicit differentiation, differentiate

A: When a function is not given explicitly but as an implicit equation then derivative is calculated us...

Q: The alphabet is made up of 26 letters, 5 of which are vowels (A, E, I, O, U) 21 of which are consona...

A: Given  The word TRIANGLE  To do Determine the number of different 8 letter arrangements that can be...

Q: Which of the following integrals can be used to evaluate the volume of the solid? Select all that ap...

A: The volume of a solid generated by a curve can be obtained by integrating the curve within specified...

Q: The diagram shows part of the curve y? = x+1 which intersects the axes at A and B. The area of the s...

A: given,      

Q: I need help with d, e, and f with work shown please thank you.

A: d. Given, I=∫3cosx2dx

Q: Find the solution to the differential equation that satisfies the given initial condition.

A: It is known that if we have differential equation, then to find the solution we have isolate the sam...

Q: If (2/3,1/6) is a critical point of f(x, y) = x2- In(x) + xy- 2y then (2/3,1/6) is: a saddle point a...

A: Given that (2/3,1/6) is a critical point of f(x,y)=x2-ln(x)+xy-2y2. We need to find the nature of th...

Q: Consider the double integralſ, ² , dydx. By converting to polar coordinates, the limits of integrati...

A:

Q: Find a value for the constant k, if possible, that kæ? if x 2 Is the function f(x) = 1 continuous o...

A:

Q: Which of the following is a solution of the differential equation d^2/dx^2+4y=0?

A: Given differential equation is d2ydx2+4y=0

Q: . Given dy/dx = −2x + 6, find the equation of the curve that passes through the point (2, −2)

A:

Q: 1 00 1 - Determine the value of the series 22+ 7n+ 12 a)1 d)5 e)0 4 1/7

A: Given: ∑n=1∞1n2+7n+12

Q: Evaluate the following integrals

A: Integration:   The collection of all antiderivatives of f is called indefinite integral of f with re...

Q: Consider the double integral dydx. By converting to polar coordinates, the limits of integration of ...

A:

Q: 6

A:

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is in...

A: It is given that, ∑n=1∞n59n   So, to check the series that whether it will converge or diverge, we h...

Q: The limits of integration of p in spherical coordinates to find the vohume of the region bounded bel...

A: cartesian to polar conversion x = ρ.cosθ.sinϕy = ρ.sinθ.sinϕz = ρ.sinϕ

Q: find the area between two curves

A:        Definition used -             The area between two curves f(x) and g(x) -                    ...

Q: x? -dx 5 (6 – x²)

A: Given integral is ∫x2dx6-x252. The above integral can be written as ∫x2dx6-x252=∫x236-x46+x252dx. Co...

Q: 2 x? y dy dx 0 - 3x

A: Solution Given ∫02∫-3xx2ydy dxWe need to find the integration.

Q: Use vectors to find the interior angles of the triangle with the given vertices. (Round your answers...

A:

Q: Hello need help

A: Our Aim is to find the value of n so that the expression is a perfectsquare trinomial. Also we are s...

Q: Consider the function f(x, y) = 6y² + 4x² – 12xy – 4y. Then: %3D - (-1,-2/3) is a critical point and...

A: Given :             f(x,y) = 6y2 + 4x2 - 12xy - 4y Take derivative with respect to x and y :fx(x,y) ...

Q: Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine...

A: The given series is ∑n=1∞e-n

Q: The function f(x,y) = 2x + 2y has an absolute maximum value and absolute minimum value subject to th...

A: Given: fx,y=2x+2ygx,y=16x2-16xy+16y2-4

Q: I need help with this

A: Compute the derivative of fx=x3 tanx+1sinx

Q: 5) Solve for r. 2Vr + 2 – V3x + 4 = 1

A: Given: 2x+2-3x+4=1

Q: Consider the following integral: sinx dxdy By reversing the order of integration, the value ofI is e...

A: Given limits- y<x<π0<y<π

Q: Find the differential equation that satisfies the given initial condition.

A: Write the differential equation. dydxtan x=a+y1a+ydy=cot x dx

Q: Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial. f(x) ...

A: Given function-  f(x) = 4x8-4x6-5x9+1  f(x) = -5x9 +4x8 -4x6 +1 

Q: Evaluate the following integral. 39 6 I| vx dz dx dy 0 0 v2 39 6 I| | Vx dz dx dy = (Simplify your a...

A:

Q: Find the sum of the convergent series. Σ n(n + 2) 16 n = 1 Need Help? Read It

A: It is given that, ∑n=1∞16n(n+2)   We can use partial fraction to make the expression in simpler form...

Q: show all work please

A: using integration

Q: please help solve

A:

Q: Let G = 6f - g. where the graphs of f and g are shown in the figure to the right. Find the following...

A:

Q: Using implicit differentiation, differentiate the following

A:

Q: 3

A: The general form of expressing a set of values in two variables is (x,y). Here, x is the independent...

Q: Evaluate each expression. 13) log, 64 4

A: 13) Given: log4164

Q: Consider the function f(x) = 7r² – 8x. Evaluate the following expressions, and simplify your answers...

A: We have the quadratic function fx=7x2-8x. First, simplify the function f. fx=7x2-8x=x7x-8

Q: Determine the type and convergence of the Improper integral d dr. a) 3rd type (both first and second...

A: We will call the improper integrals convergent if the associated limit exists and is a finite number...

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.