Solve the integral: Seln(2x² + 3x − 4)³ (4x+3) dx A eln(2x²+3x-4)³ (2x²+3x-4) + C (2x²+3x+4)4 B + C 4 C) eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) + C

Q: Which of the following can be determined given f(x) dx = 5₁ x) dx = 5,₁ ₁ g(x)dx=7, and h(x) dx = -5

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

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Q: f(x) = Jax+b (2x²-1 if x < 2 if2 ≤ x

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Q: dx secx + 1 Transforming - -z² A 1+z² B z²+z 1-z² 1+z² Ⓒ 1- D √ -dz -dz -dz - 2z² 1+z² -dz using…

A: Here, the given integral is: I=∫dxsec…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = − 9x² - 2xy –…

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Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: 3 •√₁²³f(x)dx=5₁ ₁²9(x) g(x) dx = 7, and 1 3 h(x) dx = -5 Which of the following can be determined…

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Q: R is the region bounded by the functions f(x) = 1 - 3 cos (x) and g(x) = 4 sin (x). Find the area of…

A: Ans : A=12 unit2

Q: (b) En=1 m

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Q: Evaluate the double integral: A B D) 9|N 2 N|G m 100 3 8 •√x 1. √ √V 24 +10 2ydydx

A: Evaluating the double integral

Q: (1) y=x, y=2-\x/ (2) y=1/x², y = 8x, y = x/8

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Q: (D² - 4D + 4)y= e2x sec²x

A: Reduction of order and variation of parameter (D^2-4D+4)y=e^(2x)sec^x

Q: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

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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: We will have to find  qrea bounded by rhe curve  y= x1/2  X=4 and xaixs

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

A: Formula: Antiderivative of xn = xn+1/n+1

Q: Evaluate the double integral: A) 40 B) 60 C30 D) 80 ²² (3x² +9y²)dxdy

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Q: 1 H 0 1 2 3 4 5 6 What are the domain and range of its inverse? O Domain: {y|1 ≤ y ≤5, ye R} and…

A: The domain of a function f(x) is the set of all possible values of x for which f is defined. The…

Q: 15+0. The improper integral e* dx is

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Q: y = x Arccsc (+)

A: We have to to slove derivative

Q: Evaluate [*²*3 sin 2x dx

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Q: Which point is the center of the circle * 4x² + 4y² = 4y - 8x + 5? (-1,-/-) (1,-1) 2 2 Option 1…

A: This question is based on general equation of circle.

Q: Use the intermediate value theorem to find the value of c such that f(c) = M. f(x) = = x² - x + 1 on…

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Q: Evaluate the double integral: A 9 2 5 2 (В с D m|w 416 5² 5²² 2ydydx

A: A detailed solution is given below.

Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A unitz Ⓡunit² unit2 1 D 4 -unit²

A: We will integrate the f(x) between limits 0 to 1.

Q: If g(x) == [e'-In(2t+1)]dt, find g''(x) . dx A ex-In(2x+1) 4 B (2x+1)² 4 (2x + 1)² 2 D (2x + 1)²

A: Here given that: g(x)=ddx∫-1xet-ln(2t-1)dt Using the Fundamental Theorem of Calculus: g(x)=ex-ln…

Q: A drug is injected into the body in such a way that the concentration, C, in the blood at time t…

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Q: Give the domain and range. Then, use the graph to find (a) f(-2), (b) f(0), (c) f (9) 1 (2) Ay Q 40…

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Q: Let one week's supply and demand functions for gasoline be given by p= D(q)-294-39 and p = S(a)= a,…

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Q: Consider the solid formed by the boundaries outside the elliptic paraboloid x² + y² = z and inside…

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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: Horizontal element

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

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Q: d) S tanrd. cos³x

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Q: Determine the area bounded by the functions f(x) = (x+1)³ and g(x)=x+1, 3 (A) Žunit² 1 -unit² -unit²…

A: We need to find area.

Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

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Q: Evaluate the integral: A B C D 16 1 "Im =|m 1 7/6 دان داww 3 sin(3x)cos(3x) dx

A: We have to find out integral

Q: Determine the integral: x²cosxdx A x²sinx + 2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C C…

A: integration

Q: Use of an Auxiliary Variable Solve the equation. The sum of two positive numbers is 2. Find the…

A: see below the calculation

Q: A lighthouse is on an island 500 meters off shore. The lighthouse beam makes a full turn every 9…

A: A lighthouse is on an island 500 meters off shore. The lighthouse beam makes a full turn every 9…

Q: determine all inflection points of x^4 + x^2

A: Let,  f(x)=x4+x2 Now, f'(x)=4x3+2xf''(x)=12x2+2

Q: The improper integral A e B 0 C D) 1 + ∞ [** 0 e-x dx is

A: The given improper integral is: I=∫0+∞e-xdx

Q: Find the slope of the line if it is defined. Through (6,10) and (6,-3) Select the correct choice…

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Q: The sum of two numbers is k. Find the minimum value of the sum of their squares.

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Q: Question 5 -S_(x + 1) dx A B (x + 2) (x - 1)² = √ [1+2+ = ²1+ x-1 If B -ia 9 9 W|N 1 9 3 1 9 3 دا |…

A: find out the value of A,B and C

Q: CALCULUS 2 1200-1330 TTh CALCULUS 2-FINAL TERM Exam 90 minutes remaining Oi Test Content Question 1…

A: Solve it

Q: Find the absolute maxima and minima of the function on the given domain. T(x,y)=x² + xy + y² - 6x +7…

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Q: Evaluate the double integral: 2 √² √ (3x² +9y²) dxdy A 40 B 30 C 60 D 80

A: Double Integration by iteration:

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

A: To find the solution for integral

Q: (в B f(x)g(x) dx = [ f(x) dx g(x) dx]

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Q: Evaluate the line integral, where C is the given curve. Lexy² ds, C is the right half of the circle…

A: Solution: I=∫cxy4ds

Q: Evaluate the integral: sin(3x)cos(3 A - B C D H|ო 3 16 +16 dx

A: