32 2 f is continuous and | f(t) dt = 6, find the integral / t* f(t) dt.

Q: In x2/25+ x² dx , we let x= 5sine. T True F False

A:

Q: dæ Evaluate: 9x² + 4 A None of the given choices B f (x) = -4 ln 9x² + 4 + 2 + C f (x) = -2 ln 9x2 +…

A:

Q: IVy+1-2dy can be evaluated conveniently if we let x =VVy+1-2 and dy = 4x(x² +2)dx. T True F False

A:

Q: 2 2 y 6 L72 L48 yzdxdzdy =

A: Topic = Integration

Q: J1 (3x -1)3 * tvt2 +1 dt

A:

Q: All continuous functions have antiderivatives. If f and g are continuous on a <x < b, then "Ư(x) +…

A:

Q: Question 13 - [x²/25+ x²dx , we let x= 5sine. (T True F False

A: We have to find integration

Q: S sec?x csc²xdx O None of the choices tanx + cotx + C O - tanx + cotx + C O - tanx - cotx + C O O

A:

Q: (2х+3) dx (x2+3х-6)9

A: ∫2x+3(x2+3x-6)9dx=∫(x2+3x-6)-9 (2x+3) dxusing formula∫fn(x) f'(x)dx =fn+1(x)n+1+chere, f(x)=x2+3x-6…

Q: 4. Find the area of the region that lies under the graph of f over the given interval. a. f(x) = 2 -…

A:

Q: dy -by implicit differentiation dx Given 4x -9y =1. Find

A: 4x2+9y2=1

Q: S sec°x tanºx dx

A:

Q: Find the Area bounded by the curves y? = x and x = 2y – y².

A: Draw the graphs of the given curves and mark the intersection area.

Q: If D is the region enclosed by 4 < x? + y? < 9 and y <0, then which of the following is the setting…

A:

Q: Evaluate: / y6 sech(e7hny) tanh (e 7Iny) dy A) -sech(y?) +C 7

A: We know that    elnx=  x we use above result to determine the integral

Q: 1 In solving the antiderivative of f(x) = 3sin(x) + 4cos(x)+ 5 by miscellaneous substitution, the…

A:

Q: Find the values of a and b for the curve x'y+ay =b if the point (1,1) is on its graph and the…

A:

Q: x² + 64 Using trigonometric substitution, given dx, the simplified form of the integral is: […

A:

Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1 A True False

A: We have to state whether the given statement is true or false and its reason is given.

Q: If 54 = the determinant of the matrix below. 3 -4 What is the value of x?

A: We can solve this as follows:

Q: Find the maximum point for the function f(x) = 1 + 12x – 4x O (-1, -7) O (2, -7) O (0, 1) (1, 9)

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Given problem:- Find an equation of the plane with the given characteristics. The plane passes…

Q: Write Tif the statement is true, or F if it is false. Write your answers on the blanks. dx x +C 3 2.…

A: 1.∫5x233dx=∫53x23dx=53x5353+c=x53+c1. T2.∫-45x544dx=-45x944×49+c=-5x94+c2. T

Q: a* (9x" – 10) | The antiderivative of f (x) = - is F (x) where "a" is equal to %3D 30 A 4 В 1 12 1 D…

A:

Q: Find h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

A:

Q: Question 9 In Sx²/25+ x²dx , we let x= 5sine. (A) True (B) False

A: If x=5sinθdifferentiating On both sides.dx=5cosθ∫x225+x2dx=∫(5sinθ)225+(5sinθ)25cosθ…

Q: In x²/25+ x² dx , we let x=5sine. A True

A:

Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: I have stated the used formulas in the solution

Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

Q: A circle with centre C has equation x² +y² – 6x+4y+4 = 0. (a) Find (i) the coordinates of C, (ii)…

A:

Q: Sketch the region of i nd change the order of integration ntegral 9. 3 f(x, y) dydx

A:

Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: UsinG PYTHAGORE AN IDENTITY, SOLVE FOR [sin Gx) - cos (Vx)] - 3x5 COS

A: The integration of the integral is  [sinx1/3-cosx1/3]2/(3x2/3).

Q: Give the VALUE only. No need to include the unit. * Let s, =15r +10r + 20 and s3 = 5t² + 40r, t20,…

A: We have to find time when velocity of both cars will be equal

Q: Is Rolle's theorem valid for the function f(x) = Vi-x on the segment [-1,1]? a. No since the…

A:

Q: The shaded region R is bounded by the lines x = 0, y = 0, and the curve y = x² – 2x + 2 as shown in…

A: Here, the volume is: V=∫03π(y)2dx =π∫03x2-2x+22dx=π∫03(x-1)2+12dx

Q: d d. Calculate ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt dt the product…

A:

Q: 4.Describe the largest set S on which it is correct to say that f is continuous S (x,y) = In(1–x² –…

A: Given problem:- Describe the largest set S on which it is correct to say that f is continuous C.…

Q: Find dy dx 1-Ln(»+さ)=かげとxッ) tュx 2- Y= (1+x)

A: As per bartleby guidelines we only give first question answers.

Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: Vx² –25 The antiderivative of dx is x2-25- sec lx+C. A) True B False

A:

Q: sin x Let g(x) = 1 ot. Find the derivative d'(x). '2 1+t3 none of the choices cos X 1+ sin3x sin? x…

A:

Q: a. Draw the fuunclion y=1x1/

A:

Q: x² +64 Using trigonometric substitution, given - dx, the simplified form of the integral is: sec ede…

A: ∫x2+64x2 dxput x=8tanθdifferentiate on both siddx=8sec2θ dθ

Q: 1.) f (x) = 10x10 4.) f (x) = %3D 2.) f(x) = x² – 9 5.) f(x) = 2x² + Vx 3.) f (x) = –x5 – x-3 – - x

A:

Q: Find the general solution of the following differential equation: y" + 4y" + 4y = 0. %3D

A:

Q: dr Evaluate: EV9 + 4 A f (x) = = - 9r² + 4+2 +C 3x B f (x) = -4 ln 9x² + 4+ 2 +C 3x ©f(r) = -2 In…

A: A detailed solution is given below

Q: Solve the following Initial Value Problem: y"+ 16y 0, x)= 2 and y'() = 5. %3D

A: Topic = Differential equation

Q: Question 8 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. (A True…

A: We can evaluate the given integral by using the substitution u = csc (5x)

Q: In solving the antiderivative of f(x) = sin(x) + 3cos(x) + 3 by miscellaneous substitution, the…

A: Given the function,        fx=1sinx+3cosx+3