Find Surfa ce the Area Of the 2y + X + 2 z= 2 =D2 Hint : in identifying S consider that we do the question like this S: n= 2- 2y-2z² h(y, z) 2.

Q: dx (V32 + 4)3

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Q: 1 Find the area between y = 2x and y = 2x° from x= 0 to x = . 2° The area is (Simplify your answer.)

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Q: dx (x+1)Vx²+2x

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Q: 2x Use substitution to evaluate the integral dx (x² + 3)°

A: We have to apply rules of integration to solve the problem Power rule: xn =( 1/n+1)(x)n-1

Q: dy Calculate dx You need not expand your answer. E+2) x- O a. Ob. 1 Vx + 4x /x + x, Oc. x + 1 4 d.…

A: Product rule of derivative is : (d/dx)(f•g) (f • g) ' = f ' • g + f • g ' Here f ' = d f / d x and…

Q: [IMark] a. b. f(x)dx c. f(x)dx d. f(x)dx y = f(x) Area = 1.5 %3D Area = 0.8 %3D a d Area = 2.6 %3D

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Q: O is the center of the regular decagon below. Find its area. Round to the nearest tenth if…

A: The figure

Q: Show that, cosh-1 x = In (x + /x² – 1)|

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Q: 2- Find the shaded area of the regions in the figure below 21 y = sec2t y = 1-1 TT 4

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Q: 4 Find the centroid of the next plate area Yes Yo y x A₁ -x C₁ X₂ C₂ A₂ X

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Q: Finds 2) S 12x-31 dx

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Q: 12

A: Green theorem:

Q: y =z² y = r³ - 12r Which of the following gives the shaded area? ........

A: If we have two curves y= f(x) and y=g(x)  such that f(x)>g(x) then the area between them bounded…

Q: [2y - (y2 - 15) ]dy -3 В. 5 2ydy + J [y2 - 15]dy -3 с. 5 J [G? - 15) - 2y]dy -3 D. 10 J (2y- (y2 -…

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Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

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Q: The integral dæ appears on our list of basic antiderivatives. What is the result? arctan(x) + C…

A: 1. The given integral, ∫11+x2dx2. ∫x1+x2dx

Q: Evaluate the line integral g. xy? dx + 2x²y dy, where C is the triangle with vertices (0,0), (2, 2),…

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Q: 4x -1 dx. b) x(x² + x- 6) J

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Q: dx 7. JIVa² – 2x + 5 (hint: let æ² – 2x + 5 = (z – x)²) -

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: SHOW COMPLETE SOLUTION. PLEASE MAKE THE SOLUTION/HANDWRITING CLEAR.   THANKYOU!

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Q: Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle…

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Q: C -dx(use 2 decimal places, no 5+x Let * = 2.06, and y = 1.32. Determine the value of when you…

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Q: Exatuate the integral QUS √3x xام واح

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Q: Find the area of the shaded regian of the fig- shown below. Area=[JAA LA=d Xdy * Horizantal Slice…

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