Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

Q: Find the maximum value of f(x,y) = 12-x² - y² on the line x + 2y = 5. The maximum value of f(x,y) =…

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Q: The area between the curves f(x) = x², and g(x) = 1 O 1/2 sq units O 1/4 sq units 4/3 sq units 1/3…

A: Topic:- application of integration

Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

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Q: 2 So ² ( x 7²2)² Using Trapezoidal method Blank 1 Add your answer -dx for n=4 is equal to Blank 1…

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Q: A tumor is injected with 0.6 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an…

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Q: Set-up the integral for the area of the plane region bounded by y=x+4 and y=x²-2x (x²-3x-4)dx (5+…

A: The given region are:y=x+4 and y=x2-2xTo find the area.

Q: Evaluate the following integral 1. y4+2y²-1 √y dy; y to 2. f(−4t + 12) (5t +15)dt

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Q: 4. General solution of dy= y-x dx y+x

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Q: 3. Which one of the following statements is CORRECT? A. ff(x) dx + f(x) dx = 0 B. ff(x) dx-f(x) dx =…

A: These statements are related to properties of integration. Here, We will use some integration…

Q: 3. Let R(t) = (t², 1-t², t) and r(t) = cost. Determine the parametric equations of the line tangent…

A: Here, R→(t)=t2,1-t2,t, r(t)=cos t So, F→(t)=R→∘r(t)⇒F→(t)=R→(cos t)⇒F→(t)=cos2t,1-cos2t,cos…

Q: The area of a circle of radius a can be found by the following integral a. f (a²-x²) dx √a²-x²dx O…

A: Given

Q: 9) (x - 2)² 16 9 (x+5)² ¸ (v+3)² _ 1 = + 25 16 +(y-1)² = 1 11) 2 x² X 13) 121

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Q: (x-3)² (y-4)² - + 16 196 = 1

A: Given query is to find the conic form.

Q: Given cos(8): = B 5 and the terminal side of 8 lies on the fourth quadrant. What is the value of sin…

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Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. 8 [+][…

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Q: The area in the first quadrant bounded by y = x², the circle x² + y² = 2, and the x-axis is equal to…

A: We have to find the value of a and b.

Q: If f(w) = e f'(w) = sin w+ 4 cos w find f'(w). Use exact values. J

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Q: If w = 2x² - 2y + 3z + sint and x-y=t, find the partial derivatives below. aw a. (3) X.2 c. (H) b.…

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Q: dx √x-3√x X ffv)dy, find fly)

A: solution:-∫64729dxx-x3dx=∫64729dxx12-x13dxlet x=y6 or y=x1/6x=64,     y=641/6=2x=729,…

Q: a. create a maclaurin series from the function: f(x) = 1/(1 + x)2 b. Determine the value of X so…

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Q: approximation, solve for the following functions. Show the complete procedure in calculating your…

A: Note:- These are multiple questions and according to our company guideline we can do maximum 1…

Q: f(x) = In X X

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Q: inverse laplace S 2 22 sa² + b²

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Q: termine the derivative of the following implicit function on a separate sheet paper, assuming that…

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Q: 10) (x + 7)²_ (y + 4)² = 1 + 81 36

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a horizontal element, the total…

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Q: How can the shares be divided among 30 people when the total amount is 6 million and how much is the…

A: Solution: Total Amount = 6 million Total people = 30

Q: differentiate y = ln(lntanx)

A: y=ln(lntanx) We know that, ddx(lnx)=1x

Q: A dam has a semicircular gate with diameter 4 m. The top of the gate is 8 m below the surface of…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the volume of the solid obtained by rotating the region bounded by y=x+1 y=0, and x=2 24π C.U.…

A: Answer is 9π c. u.

Q: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

A: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

Q: ind a value c that verifies the conclusion of the Mean Value Theorem for the function f(x) = x² on…

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Q: Let C(x) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands of…

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Q: Solve the following boundary value problem using finite difference method given that…

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Q: y"-2y'-8y = 0 if y(0) = 3; y'(0) = 6

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Q: Use substitution to find the indefinite integral. 16t-8t² dt (1-1) e 16t- ... Describe the most…

A: Solve the following

Q: Using Rationalizing Substitution S O Arctan(y) + C Ⓒ2Arctan(y) + C O In(y) + C O2ln(y) + C dx X√√x-1…

A: The integral is  ∫ dxxx-1=∫f(y)dy

Q: Using Rationalizing Substitution x+1 -dx = y² + 4y+ 4in(y-1) + C. express the final answer in terms…

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Q: 81-2 da Evaluate the integral: √√81 (A) Which trig substitution is correct for this integral? Ox = 9…

A: Solve the following

Q: Evaluate using the method of trig substitution 6. S dx √16-x²

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Q: Compute the total area A of the (infinitely many) triangles in the figure, if the height h of each…

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Q: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e-0.21x,…

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Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: Use the given the function: (z+2)(x-3) f(x) = (x+1)²(x-2) to answer all of the questions below.

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Q: 3) Draw the missing figure on the sequence below and provide solution/explanation:

A: Follow the procedure given below.

Q: An oil refinery is located on the north bank of a straight river that is 1 km wide. A pipeline is to…

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Q: What is the slope of the tangent line to the graph of x^2-4y^2 + 2x + 4y = 8 at (4, -2)?

A: According to our guidelines In case of multiple questions we are supposed to answer the first…

Q: Differentiate. 3 f(x)=x In 5x f'(x) =

A: The derivative of lnx is 1/x

Q: In The value of the definite integral flm 12 √ex - 9 dx is in the form F(b) - F(a), where a JIn 9…

A: To evaluate: ∫ln⁡9ln⁡12 ex−9dx Let I =∫ln⁡9ln⁡12 ex−9dx Given: ∫ln⁡9ln⁡12 ex−9dx = c3-dπ Let ex−9=…

Q: Evaluate the integral: S dx (x+6)(x-4) ← +C

A: Given problem:-