1. Find the antiderivative a) S(eš* – ) dx b) Se-4*dx c) S Vx(2 + x²) dx d) S-2xe10 - x² dx e) S 5(5x - 1)-3 dx

Q: Find the most general antiderivative. X - dx ..... O A. - 3x2 - 3x3 +c 1 x* O B. 1 +C 2x - 4 4. 3x…

A: W we have to solve the integration

Q: 8. Integrate by parts: a) St csc? t dt b) S x2 In x dx

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Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: By algebraic substitution, the integral - dx dx is converted to: 4+x 2ydy (A y+4

A: Option a is the correction and other option does not satisfy the given conditions

Q: Evaluate the double integral : 2 e2y+a dy dx

A: In double intregation, first evaluate with dy and then evaluate integral with respect to dx

Q: Find af af and f(x, y) = etry In(6y) af 4yln(6y)e^(4xy) af 1/ye^(4xy)+4xIn(6y)e^4xy dy f(x, y) = cos…

A: In the first part the answer is correct but you have mistakenly not taken bracket for 1/y . You can…

Q: 1 To evaluate the integral dx, we (x2 + 2x)3/2 sec 0 1 substitute

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Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: • If u = x+ 1 t= yu y = -t² then, %3D 1. dx dy -1 dy = X dx dy 3. dx |3D dy 4. dx 1 O 2 O 3 O 4 O 1,…

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Q: I. Evaluate the following integral: 1. S dx 3 2х+7 2. S y²e2-2y* dy 3. S sec? (4 – 3x)dx

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Q: 10 Use a suitable substitution to integrate the following. a. J/7x + 4dx b. fx' Vx' + Sdx c. (In x)²…

A: The given integration is  I = ∫x2x3+53dx

Q: Find the particular antiderivative that satisfies the following conditions: dy/dx = 6x^(-2) +…

A: detailed solution is given below

Q: Find the most general antiderivative. 9 dx -x2 x zX - IN

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Q: Find the particular antiderivative that satisfies the following conditions:…

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Q: 5) Find the general antiderivatives for the following; х-1 dx x* +2х-3 -dx 6)

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Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: Using an appropriate substitution, 3 the integral S dx equals: /1-4 (х-1)2

A: Here we have to evaluate I=∫31-4(x-1)2dx

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: dy – 5x-2+ 2x-1 – 6; y(1) =7. dx |

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Q: Hiws slove du 4 dt %3D dx2 u(6,t) = L (8,t)=0 U(x, a) =0 : =4X-()x²

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Q: (ii) o S(2xy + z)dx dy dz z=-1 :0 Jx=1

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Q: What is / - z dx? 1-x² o f- dx = -2cos-lx + C V1-x2 S- dx = 2sin-lx + C (1–x2 S-d 2 dx = 2cos-x + C…

A: 1. I=∫-21-x2dx =-2∫11-x2dx =-2sin-1x+C    ∵As ddx(sin-1x+C)=11-x2⇒∫11-x2dx=sin-1x+C=-cos-1x+C…

Q: Evaluate xy z? dx dy dz

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Q: Find the antiderivative of dx / (25 + 4 x^2) * O (1/2) arctan (x/5) + C O (1/10) arctan (2x/5) + C O…

A: An antiderivative is an integral process that can help a function to get back into its parent…

Q: 2. Use the substitution u = x² and then Integration by Parts to evaluate / x³e**dx.

A: Given: ∫x3ex2 dx We substitute u=x2, that implies du=2x dx. By using this substitution, ∫x3ex2…

Q: Evaluate the iterated integral. 7 8 (x² + y² + z²) dx dy dz -6 0 0 7 8 (x² + y² + z² )dx dy dz =

A: Given that: ∫-66∫07∫08(x2+y2+z2)dxdydz

Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, dv is set as: O ex dx O…

A: We have to find the dv

Q: 9. Use integration by parts to show that pP+1 ]n°(x) |aP In°(x) dx p+1 p+1

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Q: Evaluate the iterated integral. 4 5 6 (x² + y² + z²) dx dy dz -4 0 0 5 6 (x + y? + 2? )dx dy dz = i…

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Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

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Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: 1. Obtain the par hicul ar foluhon 4 DE . 9xy dy a. oy dx = ; uh en x= 2,y=1 b. 4xy dy = 2y (I+ y?)…

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: 4. Use Green's Theorem to evaluate | ay dx + (1 – ry) dy where C is shown below y (14) F1,2), (1.1)…

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Q: Find the particular antiderivative that satisfies the following conditions: dy 4x-2 + 2x-1 – 7; dx…

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Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: E valvate cox³ (x²+3)dx 2.

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Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation dy +y dx = 3x?y? becomes dz…

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Q: Evaluate the Double Integral. 4 V16-x2 b. 2x dy dx

A: We have to evaluate

Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).

Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5

Q: 2. Compute and x² - y² (x² + y²)2dX(y)dX(x) [0,1] [0,1] 0.1 - San Sas (2² +2²³)2 A(z) dx (1). [0,1]…

A: Here, in the question, two integrals are given. We have to explain why both the integrals do not…

Q: In item number 5, the integral of Sx3 dx is obtained by applying what Basic Theorem of…

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Q: b) Evaluate the triple integral S dx dy dz re3 1 xyz

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Q: th 2 Evaluate khe fulawingcartesian integrat by changing theminte equiv alent Pelarintegrals: E 4-y…

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Q: Evaluate the iterated integral. 2 4 (x2 – 2y2) dx dy 1 Jo

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