What is the area under one crest of the sine curve, from x = O to x = n? y=sin x dx 1/2

Q: Evaluate: (4) S esc" (a) (2x +1) dx C6) Syos y dy

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Q: The graph of F(x) is shown below. The areas of the shaded regions from left to right are 265, 20, 28...

A: Let's find. 

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t? from t = ...

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. dy V12y +1 +C

A: we need to evaluate the integral :  

Q: 7. (1+x*)dy + x(1+ 4y°)dx =0

A: We solve question no. 7n, because in 6 statement not corect one extra (+) showing in (x++√y)dy,pleas...

Q: Consider the following. f(x) = 6x3 – 9x? – 108x (a) Find the intervals on which f is increasing or d...

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Q: Question 11 Evaluate the integral Jve'dy. A Enegative 1 half e to the power of y squared end exponen...

A: Let's find. 

Q: Tell if the following infinite series converges or diverges n=1 |cos(nn) Vn+1 Answer: It is divergen...

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Q: ,5x-2 If f(x) = 2 + e%r-2 %3D then f-'(3) = %3D

A: Topic = Functions

Q: Growth of a Cancerous Tumor The volume of a spherical cancerous tumor is given by the function V(r) ...

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Q: cos2t dt Evaluate the Integral (1+ sin2t) 4 A (1+ sin2t) 3+ C (1+sin2t) -3+ C 6. (1-sin2r) 3+ C 6. D...

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Q: dx Perform the Integrations 1+ sin x+ cos x Use the editor to format your answer

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Q: Suppose 4x2 + 16y2 = 100, where x and y are functions of t. dy (а) If dt 1 dx find when x = 3 and y ...

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Q: 5 In each of the following, show all points and vectors graphically, and express the indi- cated vec...

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Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per second...

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Q: fx*In xdx 34

A: The objective is to evaluate the integration.

Q: Use the First Derivative Test to find the local maximum and minimum values of the function. (Enter y...

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Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflect...

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Q: Evaluate the integral. V36 – x² dx = 18sin- +xV36 – x² + c V36 – x² dx = 36sin--xV36 – x² + C / V36 ...

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Q: List the values of x at which f has a local minimum. Select the correct choice below and fill in any...

A: Lowest points of all ,after that function start increasing is called local minima.

Q: xsin-xdx The antiderivative of -V1-x2 sin-!x +C A True B) False

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Q: Find the area of the region between the parabola y=64 - x² and the x-axis. Round your answer to thre...

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Q: dr = Blank 1 Evaluate the Definite Integral 0. I+8x Blank 1 Add your answer

A: A detailed solution is given below

Q: Find the coordinates of the centroid of the solid generated when region bounded by x? + y? – 4y = 0 ...

A: The given curves are: x2+y2-4y=0 y=4-x

Q: The amount of a new allergy drug, nalamox, decreases by 26% every 4 hours. (a) Determine the 5-hour ...

A: Given: For (b), So, for 1 hr decrement in % is 26/4=6.5%. For (a), For 5 hr the change factor is 26...

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate ...

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x...

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Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where approp...

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Q: 89. Find the coordinates of the centroid of the area bounded by x² + y? – 4y = 0 and y = 4 – x is re...

A: The given curves are: x2+y2-4y=0 y=4-x

Q: Find the volume of the solid generated bounded by x = Vy – 1, x = y² – 2y + 1, rotated about the x- ...

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Q: da 3. S algebraic substitution (x-3) Va-4

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Q: If f(x) = 6 cot +4, then find the value of f'(-4) is

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Q: 43 dx Blank 1. Without any computation, find the values of %3D Blank 1 Add your answer

A: Given integral can be solved by applying power rule

Q: Evaluate the integral

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Q: Find all critical values and critical points of the function given, then find the regions where the ...

A: The answer is in step 2.

Q: 7 > k(2k + 1) с. k=1 7 2 7 k3 d. 4 k=1 k е. k=1

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Q: Do the following for the function f(x) = 6x? + 5x. (a) Express the slope of the secant line in terms...

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Q: solutions

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Q: Evaluate thne integr sec3xdx A 3ln sec3x+ tan3x +C In sec3x + tan3x +C C =In sec3x- tan3x + C In sec...

A: Solve the integration

Q: S* (1– x)e* dx

A: To find out the integration. 

Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² – ...

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Q: 6 The coefficient of sin( 2x) in the antiderivative of F(x) = cos is Blank 1 (use fraction form not ...

A: ∫cos6(x2)dxsubstitute u=x2→dudx=12→dx=2du=2∫cos6u du=2[cos5u.sinu6+56∫cos4u du]=2[cos5u.sinu6+56[cos...

Q: Let v = (5,7). Which of the following is the direction of v? Arctan Arctan Arctan Arctan

A: Given v=(5, 7) We have to find direction of vector

Q: Evaluate the Definite Integral sin'y dy = Blank 1 Note, the answers should be three decimal places o...

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Q: Find the most general antiderivative. A B D

A: Let's find. 

Q: (x² – 1)*dx

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Q: 4Vx + 2xVxdx X

A: ∫xn dx = xn+1n+1+C ∫af(x) dx = a∫f(x) dx

Q: A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft from the...

A: This question is based on application of derivative.

Q: Column A 1. xy = 2 3x²y – x = 5 3. 3y(y – 10) + 24x = 0 4. (x - y)? = x + y - 1 5. 2/xy = 3 x+y = X ...

A: We will use simple differentiation rules to solve this question.