1. Use calculus to compute the integral / (3r + 5) sin(r)dr. 2. Use calculus to compute the integral In(z)=dx. 3. Use integration by parts to compute the indefinite integral -× dx 4. Evaluate 4x³e* dx.

Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4.

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Q: 4) 98)=(40*– Bu) 5 %3D -

A: Given that      g(u) = (4u7- 8u)-5

Q: The antiderivative of f(x), denoted by Fx), exhibits an odd symmetry i.e., it satisfies the property...

A: we have to find the anti derivative .

Q: cos2x – sin2x cos2x - dx=- + C• What is F(x)? For cosx – sinx 2 sinx - cos?x – cosx+ sin³x 3 3 (sinx...

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Q: cos2x - sin2x cos2x For dr==F(x)+c What is F(x)? COSx - sinx O (cscx- secx) 3 2 2. sinx +-cos'x+cosx...

A: Given:          ∫cos2x-sin2xcos2xcosx-sinxdx=13Fx+C      =∫cos2x-sin2xcos2xcosx-sinxdx   Expanding t...

Q: Find the general solution to this homogeneous equation using the auxiliary equation method y”+ 4y’ +...

A: The given differential equation is  y''+4y'+8y=0.

Q: Find the area of the triangle with vertices P(1, 4, –3), Q(0,0,0) and R(3, 5, 1). NOTE: Enter the ex...

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Q: dx - = In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-lx+ 1)

A: Let's find. 

Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: ch of the following integrals is equal to the integral / f(3x-5) dx? ) dr? 7/3 ) dz

A: Please refer to the image below

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i + 4j. NOTE: Enter the exact answe...

A: Given :Make an angle of 45° with 7i + 4j

Q: dx Evaluate 3x – 12 O - 00 + 00 1

A: Let's find. 

Q: dx 14. Evaluate Зх — 12 A.ο В.1 00 D.0

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Q: | 120 sec(a + 10) tan(a + 10) da .3

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Q: b. d xP +C. What is the value of the sum a The general antiderivative of (3x2-4) 2x2 can be written ...

A: ∫(3x2-4)2x2dx=∫(9x6-24x4+16x2)dx                             =97x7-245x5+163x3+c

Q: dx -= In[F(x)]+C. What is F(/3) For (x+x³) (x Tan-lx+ 1) 3. B.

A: We have to choose the correct option according to the given information

Q: Find the area of the triangle with vertices P(1, 4, –3), Q(0,0,0) and R(3, 5, 1). NOTE: Enter the ex...

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Q: sec. sec A x2 + 1 x2 +1 2x Option 1 Option 2 x² – 1 x2 – 1 - 2x Option 3 Option 4

A: Given secA+tanA=x To find secA:

Q: 4-z4 Find dz where I is a circle z-2=5. (z-4) 4 - 96 Tti - 32 T 32 Ti 96 Ti A Moving to another ques...

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Q: cos2x – sin2x cos2x - dr = -F(x)+C. What is Fx)? 19. For cosx – sinx 3 A. (cscr - secr)3 2 2 sinx - ...

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Q: (2- sec?x) " sec(3А — х) e In (a le) sec3x -dx to be integrable using What should be the value of A ...

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Q: cos2r – sin2x cos2r For -dr=-F(x)+C_What is F(x)? cosx – sinx 2 sinx + -cosx +cosx+ =sin³x 3 3 O (cs...

A: We know that,  Int(sinx)=cost Int(cosx)=-sinx

Q: I. Solve the following: 1. Given: y = 2x - Find: a.) dy/dx b.)y" 2. Given: 16y – 9x? = 144, find y" ...

A: Given  1. y=2x-13+43x-2 if x=22. 3x+4y3=5 If (3,2) To find slope m:

Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

A: Definite integration

Q: dy +x =

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Q: I Solve the ff. problems using trigonometric or inverse trigonometric functions Show illustration, d...

A: maximize the function

Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

Q: Choose among the following tests ONLY: integral, comparison, and limit comparison to determine if th...

A: We have to check weather the given series is convergent or divergent

Q: CHAIN RULE DERIVATIVES Date Directions: Differentiate the given functions. 2.) G(X) - T52"

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Q: 2x +4 9. Let f(1) = Find the equations of the horizontal and vertical asymptotes of %3D 5x +2 y = f(...

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next ti...

Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4. A 21/2 square ...

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Q: The antiderivative of fx0, denoted by Fix), exhibits an odd symmetry ie., it satisfies the property ...

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Q: Find the area of the region bounded by the curve y=1--x? and the x-axis. 8 square units 4 square uni...

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Q: 3. Which of the following is an improper integral? -dr -4 x²–x- 2 А. In3e COSX хе 'dr В. dx c. 2x+ 8...

A: Given problem:-

Q: y'dx +e* dy = 0 e* +y =c Ans.

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Q: (1x) +3 . Is-3 Check the continuity of f(x) ={-2x , -3 <x< 3 12 3 (6x + 2 ,

A: Here we have to check the continuity of the given function f(x).

Q: The integral of the function below may be written as me" sine) + px + qe* + C. Wherg. m,n, p, q,r an...

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Q: Question 5 dx - = In[F(x)]+C.What is F(3) if C= 0? For (x+x*) (x Tan-lx +1) 1 A B 3 1 D

A: Integration is the act of bringing together small components into a single systems that functions as...

Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: 6) yo Do° (7C +2)"

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Q: Show that the equation x – 18x + c = 0 has at most one root in the interval [-2, 2].

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Q: What is the integrable form of dx? du u2 du np u²) 2 du

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Q: 4. Starting from the same point, Royden starts walking eastward at 0.5 m/s while Nilo starts running...

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Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the c...

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Q: 2 + x², -2 <x< 0 1. f(x)dx; f(x) = -x + 2, 0<x<4 -2 2

A: Given query is to find the value of the integral.

Q: 6. f Vesx + etx dx

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Q: Evaluate the derivative of f(x)=√x2-1, using the formula:

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Q: Let f (x) = ax- 5/12 + 4x2. Find the value of a if f' (1) = 26. %3D

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Q: d?y =6-9x and which passes through the points (0, -1) and (2, 3). Find the equation of the curve for...

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Q: Find the diameter of the circle 4x? + 4y? + 24y – 4x – 35 = 0. A. 6V3 B. 6V7 C. 3/6 D. 37 E. None of...

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