.b if f is continuous on [a,b], and f(x) 20 then √VF(x) dx = f(x) dx T True F False

Q: Evaluate the triple integral: A) 18 B) 24 C) 12 D) 6 3 2 S²³² S²(x+y+z)dydxdz 0

A: We have to find the value of given integral

Q: y" - 3y' + 2y = 6

A:

Q: (x+1)dx (x+2)(x-1)² S A 2 - x+2 B -1 + (x-1)2 ]dx. the values of A & C respectively are:

A: integration

Q: Find the area bounded by x² = 4y + 4 and x = y - 2. Using vertical element, what is the integral…

A: The area bounded by the curves x2=4y+4 & x=y-2 is:

Q: sinh xte cosh x + ndefinite Integral Sin(cosh x + e*)- In(cosh x + e*) sinh x te cosh x + ex

A: We have to calculate the given indefinite integral according to the given information

Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

A:

Q: Q/IF 3 = sin(x) 0²³²141 y= (4) y = 3/2 I sin(x) cos(x) Prove that

A:

Q: Evaluate: dx (x+1) log(x+1)

A:

Q: dx Transforming secx + 1 2-2z² A 1+z² ® √ ₁ + 2²/1d² +z² B -dz 1-z² z²+z C / 1-z² Ⓒ / 1-²/²0 D 1+z²…

A: To find the transformation of the integral ∫dxsec x+1 after using miscellaneous substitution.

Q: The general solution of (D²-2D+1)y=2sin x y=C1eX + C>XeX + sinx By=c₁еx+c₂xe* +2sinx Cy=c₁еx+c₂xe* +…

A:

Q: The improper integral A 0 B 1 с e D 8 +∞ St 0 ex dx is

A:

Q: Evaluate the integral: e3+cosh2x33+cosh2xsinh2x dx (Α) (3e)3+ sinh2x 2+In3 + C (3e)3+cosh2x B 2+2ln3…

A:

Q: Evaluate the integral: 1 A 6 B С 3 D HIM P 16 sin(3x)cos(3x) dx

A: Solve by integration

Q: If f (x) = A (В B C D Stams. 0 sec²x tanx 1+1² Ite¹ 1+e tanx sec ³x 1+e -dt, then f'(x) equals tanx…

A:

Q: Which of the following methods can be applied to find a particular solution yp of y" +y = cos(ex)?…

A:

Q: Evaluate the following iterated integral: for-y |x - y dx dy. Answer: 1/3

A:

Q: sinh x tex + ex cosh x In the indefinite Integral in(cosh x + ex)- sinh x tex A In(cosh x + e*)-…

A: Answer: A

Q: Given the integral sec6 (x - 1) tan4 (x - 1)dx, which of the following equatio useful for…

A:

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: A detailed solution is given below.

Q: Find the area bounded by : f(x)=e*, g(x) = e¯* and x=3. A (e²-1)² e2 sq. units B (e³-1)² e3 sq.…

A:

Q: Find the area bounded by: f(x)=e*, g(x)=ex and x = 3. A (e³-1)2 e3 sq. units (e²-1)² e² sq. units…

A: Please see the below picture for detailed solution.

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A may vary depending on…

A:

Q: A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward the pole with a…

A: Given problem:- A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward…

Q: 1 √√√x + x² S- dx Solve the integral: 5in1+x² ² x ²³² | + c A C 5 n/₁+x²|+c B C Ⓒ 6in/5+x³ +C…

A: to evaluate the integral.

Q: Which of the following can be determined given Ⓒx-d A (x) - )-g(x))dx (B S (4f(x) +9h(x))dx g(x)dx…

A:

Q: Question We can apply General Power Formula of Integration on which of the following integrals? A…

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

Q: sinh x tex cosh x + ex In the indefinite Integral in(cosh x + e*)- sinh x + ex A cosh x + ex sinh x…

A: In this question, we want to know the integrand of the given Integral.

Q: V = 8TT². Which is the correct expression for dV dr dh 16ПР- dt dt dV dr = 16Tr dt dt dV = dt dV dr…

A: Topic:- application of derivatives

Q: . The daily amount of smog produced by cars coming into a city is given by y = 2 + 0.01x3/2, where y…

A:

Q: 1. ²₂(x² − 2xy² + y²³) dx dy

A: Solve the following integration .

Q: In evaluating S dx is same as evaluating lim C-3+ (In(f(x))). Determine the value of f(x) if x=3.4.

A:

Q: Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+cosh2x B 2ln3…

A:

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

A:

Q: tank has pure water flowing into It at 10 L/ min. The contents of the tank are kept thoroughly…

A:

Q: Find d2y/dx2 for y2 + 2y = 2x + 1

A:

Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; A sine…

A: On solving this we will get  To evaluate the given integral we use the the identity in given option…

Q: y = x²sin (3x)

A:

Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

A:

Q: 2x-1 a. √ (2x + 1) e ¹-¹ dx

A: The given integral is ∫2x+1e2x-1 dx We solve the integral using integral by parts formula. From…

Q: Find the area bounded by : f(x)=e*, g(x)=e*, A) (e²-1)² e² sq. units B (e²+ 1)² e² (C) (e³-1)2 e3 D)…

A: In the given problem we have to find out area of region bounded by given curve with the help of…

Q: D sec²u=1+tan²u

A:

Q: In the indefinite Integral Sin(cosh x + ex)- A In(cosh x + e*) B sinh x + ex C In(cosh x + e*)- sinh…

A:

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)= x² + 2x…

A: Using disc method, volume is evaluated.

Q: If (x+1) dx (x+2)(x-1)² 1 93 2 93 S- A B D -io 1 W|N -io 2|3 2|3 9 3 A x+2 + B + x-1 C (x-1)² (x -…

A:

Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A:

Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: Question 3 Iff is continuous on [a,b], then T True F False b then f(x)dx = f(x)dx T a

A: Here it is given that f is continuous on [a,b] From the integration we can take the constant value…

Q: What is the annihilator for y=x e*cos 2x ?

A: Our Aim is to compute the annihilator for y=x ex cos 2x -(i)

Q: Using the method of variation of parameters, the form of a particular solution pof (D²+25)y=4x²-3e5x…

A:

Q: Find the area of shaded region. 1/4 sq. unit 1/2 sq. unit T/4 sq. units 1/2 sq. units j r² = sin 20

A: The shaded region is bounded by the polar curve r2=sin2θ in the first quadrant.