If f(x) = 2[g (x)]³+7, then what is f'(x)? (A) f'(x)=6g (x) g'(x) (B) f'(x)=6g'(x) f'(x)=6[g(x)]²g'(x) f'(x)=6[g(x)]²g'(x) +7 D

Q: (A) B (C) (D) **/2 18 [*/ ces **/2 cos²0d0 18 sin²0d0 cos²0d0 0 of the 0 **/2 $ cos²0d0

A:

Q: 1 11 Given 1 [²_f(x) dx = 0 and [ f(x) dx = 1 1 ₁ ¹3f(x) dx - 2f(x)dx. evaluate 6 0 -1 55 A 6 11 B 5…

A: A detailed solution is given below.

Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

Q: What is the differential equation corresponding to the general solution y² = Cx³. dy 2y = A dx 3x dy…

A: solution:-y2=Cx3where C is only one arbitrary constantdifferentiate both…

Q: [² -dx, determine all value/values of P for which the improper integral Given converges? (A) {0,1}…

A: The integral is ∫1∞ 1xpdx

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: The limits of integration will be the interval on the x-axis for which the area is bounded.

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

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Q: √√ Solve the integral: √√x A (В 33√x² +C Ⓒ 3√/x² +6 +C D 6√√x +C √√x dx x²

A:

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

A:

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

A:

Q: (x2y3 - 1+) dx + x3y2dy = 0 1+9x2

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

Q: y = 2 sin 3x 1+3cos2x

A: We are given  y= 2sin3x/(1+3cos2x)  We have to compute y'.    Before computing y', let us first see…

Q: 1 √√√√x + x S Solve the integral: A m/1+x³²|+c C {/in/1+x²³ | +c B © 6in/5+x³³| +C Ⓒ √I/1 .…

A:

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

A: The integration are

Q: w/N Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. Revolve the…

A: Application of integration

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1 A unit2 B unit² unit² Ⓒ /…

A:

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: Which of the following is NOT a method for finding volume of solids of revolution? A washer method B…

A: Please follow the next step.

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

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: C) (-∞,1]

A:

Q: What kind of polar graph has the equation r = 3 ? * cardioid lemniscate circle rose petal

A: Solution: equation r=3

Q: How many antiderivatives does a function of the form f(x) = x^ have when n* 0₂ none 1 infinitely…

A:

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

A: D is correct option.

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A:

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

A: Washer method

Q: If a horizontal element is used to find the area bounded by y=√√√x, x=4 and the x-axis, the limits…

A:

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A 2-unit² B -unit² с…

A:

Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

A:

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

A:

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

A: This question can be solved using integration by substitution.

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.

Q: Question 6 Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1, A unit² Ⓡ®…

A: Just plot the graph and see which is above and below to each other and find intersection point

Q: y = 2 sin 3x 1+3cos2x

A: We can solve this as follows:

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming 1+z² Ⓒ √ 1 + 2/²/d= (A) -dz…

A: First of all, note that sec x=tan2x2+11-tan2x2⇒sec x+1=tan2x2+11-tan2x2+1⇒sec…

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

A:

Q: Let f(x)=√√3x-2 on the interval [ 13.1] axis about the y-axis and find the volume of the resulting…

A: We need to find volume.

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

A:

Q: An equation of a hyperbola is given. (x+3)²-(y - 3)² - 1 9 16 (a) Find the center, vertices, foci,…

A:

Q: If g (x) = — _ _[e¹ — ln(2t+1)]dt, find g''(x) dx -2 (A) B C) D 4 et + (2x + 1)2 4 et + (2x+1)2 e* -…

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: y= 3 Arcsec 3x

A:

Q: d^3-5d+4)y=0 when, x=0, y=-2, dy=9, d^2y=0

A:

Q: Which expression is equivalent to O cotx+sec x O cos x + cot a Otan x+sec x O sinx+tan x an £ ? cos…

A:

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

A: Volume

Q: Question 20 Determine the area bounded by the functions f(x) = (x + 1)³ and A unit² А 3 Ⓒunt² B 3 C…

A:

Q: Evaluate the double integral: A B NIG 5 3 m|p 99 In +10 2ydydx

A: To solve the following double integral

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

A:

Q: Using the method of variation of parameters, the form of a particular solution Yp of…

A: Here, the given DE is: (D2+25)y=4x2-3e5x