10. Evaluate the indefinite integra a) S sinxecosx dx b) Seda 1+vx

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: use the definition prove that s d sinZ %3D Tal

A:

Q: 2)Evaluate ex dA , Ris bounded by y = x2,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Evaluate the integral using FTC I.

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Q: O Calculate He in tegual usng the Caucly Integral Theoren sin b (2) dz

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Q: .2 (3 – z)(3z + 1) dz

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Q: Prove That:- o sinhz= loy (Z+lz*+l )

A: To prove, sinh-1z=logz+z2+1     Lets consider, y=sinh-1z…

Q: Сompute 1. f dx, where f(x)=|x|.

A:

Q: Approximate the following integral using three-point Gaussian quadrature rule. 2 dr 1²–4

A: Gaussian quadrature rules evaluates the integral with higher accuracy. The three point Gaussian…

Q: sho w that fQ) = x xE To,1] is Riemann integrable amm

A: The given function is: fx=x3, x∈0,1

Q: Evaluate the impropec integral oc sho that it diverges, dx

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Q: Use the definition. that sinz •prove Z = UJZ %3D

A: Using definition of derivatives.

Q: Find the integral. Show work. Inx dx

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Q: What is §3dx, §5du and §e^u dt? Those are integrals

A: a) We factor out 3, then integrate. c=integrating constant

Q: Apply Green's Theorem to evaluate the integral P (3y2 dx + 3x2 dy), where C is the triangle bounded…

A:

Q: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: Evaluate the integral: ft² ns te" du ds dt

A: Let's evaluate given integral.

Q: Obtain the moment of the area generated by x = 2a, bounded by x =y and x2 = 2av.

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Q: Find antideriuative Flx) of the an flx) = _8 sinx 13 + COSX functian such that FlO) = 1 %3D %3D

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Q: Evaluate the integral using FTC I.

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Q: Which substitution is needed to evaluate the integral S tan* x sec² x dx =? u = tan* x, du = sec? x…

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Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Use an appropriate change of variable to evaluate the double integral: cos dA, R where Ris in the…

A: Given integral is  ∫∫Rcos(y-xy+x)dAR is the region bounded by x+y=1 ,x+y=2 in the first quadrant.

Q: Use the given substitution to evaluate the integral.

A: Given integral: ∫sec22θ tan2θ dθ

Q: Use Property 11 to estimate the integral xxD esin x cos y dA, where is thedisk with center the…

A: We know that –1 ≤ sin x ≤ 1 and –1 ≤ cos y ≤ 1, Hence, –1 ≤ sin x cos y ≤ 1

Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: 19. Evaluate the integral by changing to spherical coordlihates. Rf xydzolydx

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Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxy dydx

A: We have to integrate the double integral:

Q: Apply Green's Theorem to evaluate the integral (4y² dx + 4x² dy), where C is the triangle bounded by…

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Q: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z?)dy + (3z² – 3xy + x² + 2yz)dz

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Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: Reverse the order of integratlon and then evaluate the Integral 10Tin6 Jinu! dx dy 9/10 et2

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Q: Solve the problem in a paper and upload as a pdf document. .3 Evaluate the integral SIT w?yz+v² xz +…

A: Solution: The objective is to evaluate the given integral

Q: compute J secx dr. I n trying to integrate

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Q: Find the length of x = In(sin y) from y = to y = . %3D

A: The arc length of a function is the length of a curve fy on an interval a, b given byL=∫ab1+f 'y2dy…

Q: Estimate the integral Sinx using Compostte tra pe zoidal rule with h=0.25

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Q: Use a computer algebra system to evaluate the iterated integral. V 9 - y- y dz dx dy 9 - y

A: Consider the integral:…

Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x², x = 5

A: Given ∬7x cos y dydx , y=0 ,y=x2 , x =5

Q: The suitable substitution to evaluate the integral [V tan (2x) dx is cos (2x) O u= sec(2x) u =…

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Q: Evaluate the integral using FTC I.

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Q: 7. Use contour integration to evaluate (a) dr x²+x+1² de (b) 3+2 sin

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Q: Evaluate the iterated integral. 3 (2z fIn(x) '3 xe-Y dy dx dz Jo

A: ∫13∫02z∫0ln(x)x e-y dy dx dz

Q: Use the Composite Trapezoidal rule with h = approximate the improper integral 1 sin 2x dx to

A: Given,        ∫01sin2xx3dx=

Q: Evaluate the integral. 4VE e dt Vt 4VE e dt =

A: This is case of integration by substitution where we look for an derivative in the integrand.

Q: Evaluate the iterated integral. SIT stad dy dx dz 5ze

A: Answer and explanation is given below...

Q: Write the integrand in terms of u. 2x (x + 1)' dx = du %3D Evaluate the integral.

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Q: theorem, calulate b) Using the Re si due the dz integral the Over TZ (2-2)4 Curue.

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Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.