1. The region bounded by the graph of y = 2x and the x-axis over the interval [-3, 3] consists of two right triangles. One has area (3)(6) = 9 below the axis, and the other has area (3)(6) = 9 above the axis. Hence, 2x dx = 9 – 9 = 0 6. -3 -2 2 3

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge-Kutta method, what is…

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Q: ! 6-Find the value of the integral * U x3/2 e-x dx

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Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

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A: Given: ∫1x2-4xdx

Q: 1. What should be A for the path independent of (2,4) xy+ ^ dr + 2Ay – x dx + y? fip- (1,2) Moreover…

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Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: 14. Evaluate the integral. 4 (y - 2)(2y + 1) dy

A: Given that : The integral is ∫04 ( y - 2) ( 2y +1) dy

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Q: 5. Find fSp(x + y)² dx dy, wh- region in Fig. 17.2.12. y = x

A: Answer is 7/12

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Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

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Q: 4) Evaluate the definite integral: S, (2x² – 4x + 6)dx. -

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Q: 1. What should be A for the path independent of (2,4) xy + X -dx + 2Ay – x -dy. y? Y (1,2) Moreover…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: 8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y…

A: Given:  ∫Ccosxsinydx+(3xy+sinxcosy)dy...................(i) where C is bounded by y=x4  and  y=x To…

Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: EXAMPLE 7 If it is known that F(x) dx = 14 and f(x) dx = 9, find F(x) dx- SOLUTION By a property of…

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Q: Given (1+ 3x sin y) dx – x² cos y dy = 0 with y(1) = 0. Using Euler or Runge – Kutta method, what is…

A: Given 1+3xsin ydx-x2cos y dy=0....(1) with y1=0 We will find the value of fx, y to approximate y

Q: 4х+2 Evaluate the integral -dx. (Hint: Use Algebra to help further rewrite your (x² +1)(x=1)…

A: First break by using partial fraction then integrate

Q: Question 8 Set up an integral for the length of the curve yV1+x on 2 sxs3. x2 dx 9(1+x-)5/3 x2…

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Q: 1. Evaluate the integral of x2 (3 - 2x) dx if upper limit = 2 and lower limit = -1. а. 12 b. -12 C.…

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Q: 3. Compute x' In x dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

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Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

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Q: b 2 1+(- dx dy² dx, X y= e у3е ,0<x<1 а Use COMPOSITE Simpson 1/3 rule. Use nine nodes

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Q: 2. Find the indefinite integral: S (Vã+ - x + - 1) dx 6 .3 X X

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Q: The integral of the given function | sin 9x cos 4x dx is equal. .... 13 cos(5x) — 5 сos(13x) А. + C…

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Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

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Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

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Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

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Q: 18 2 6x dx using n = 2, 4, and 8 subintervals 2

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Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: 5. The integration form of , XY dA where Dis the portion of x+Y = 2 in the 1" quadrant will be

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Q: integral x^2 e^2x

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Q: 1. What should be for the path independent of (2,4) 2Ay – x dp. y? xy + A dx + (1,2) Moreover…

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Q: 2. Use integration by parts to establish the reduction formula: Sx" cos x dx = x" sin x – n x"-1 sin…

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Q: 5. Find ffp(x + y)² dx dy, region in Fig. 17.2.12.

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Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: 2 1. Evaluate the integral: dx 2 x2-x

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Q: -X +7 Evaluate the integral: dx (x-2)(x+3) In x - 2|+2 1n x +3 +C 2 In |x – 2| – 2 In |x + 3|+C 2…

A: First of all we will do partial fraction, then we will evaluate the integral.

Q: 1 Find dy/dx for the given value of x a. y = xarccos x x= -1/2

A: Given- y=xarccosx To find- dydx at x=-12 Identity Used- Using the product rule of differentiation…

Q: 30. It is given that the graph of y=-x+mx-n touches the x-axis at one point. Suggest two pairs of…

A: Consider the following equation: y=-x2+mx-n The above graph touches x-axis. Substitute y=0 in the…

Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x du -dp y? dx + (1,2) Moreover…

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Q: 8. The area of the region outside the curve r = 3 - 3 cos 0 and insider = 6 is

A: We have to represent the required area first.

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge - Kutta method, what is…

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Q: Question 2 Set up an integral for the length of the curve y=V1+x? on 2 sxs3. x2 1+ dx 4(1+x)3/2 x2…

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Q: B. Integration by Parts 1. xcosx dx

A: We know that integration by part formula is given as  ∫uv dx = u∫vdx - ∫dudx∫vdxdx To evaluate: ∫x…