X-2 Se Evaluate the integral: (+3x-7) dx A x²+5x+In 3x-6|+C B +In|3x-6|+C C + In/x-21 +C 3 D) +5x+3ln|x-2|+C N|X x² + 5 +2²+ + 5x + x² 2

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: To find the area bounded by curves

Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

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

A: Answer: The solution is given below:

Q: 2 Let f(x)=√√3x-2 on the interval y-axis and find the volume of the resulting solid. 43x A -unit3…

A: Let's find volume of solid given curve.

Q: Solve for r in terms of P, n, and t: P = (1 + =) ² Or=(nP-1) Or=In(P)-1 Or = n(P-1) Or="(P-1) T=…

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Q: dx Evaluate: s (x+1) log(x+1) A --In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C с = -log² (x + 1) + C…

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Q: y= (sec ³x + tan ²x)

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Q: --—-^[e'-In(2t+1)]dt, find g''(x) . dx -2 If g (x) = (A) (В Ce*- D 4 (2x + 1)² e* - In (2x + 1) 2…

A: We have to solve integral

Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

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Q: Why is it "h • db/t + b • dh/dt"  instead of   "h • dh/dt  + b • db/dt"?

A: Using Rule of differentiation.

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Q: Question 9 d If g(x) = ·S*^[e'− In(2t+1)]dt, find g''(x) . dx -2 4 A (2x + 1)2 4 B (2x + 1)²…

A: Using leibnitz rule.

Q: 4 Evaluate the double integral: 2ydydx 1 A B (ⒸⒸC) D m 100 8 +10 9 2 5 2

A: On solving this we will get  Option (C) is correct

Q: Consider the following system. dx = -9x + 4y dt dy 5 -- +2y dt Find the eigenvalues of the…

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Q: Question 4 Which of the following is NOT a method for finding volume of solids of revolution? A…

A: Please see the below picture for detailed solution.

Q: dy 53.x = dx Vx2 -4, x = 2,y(2) = 0

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

A: The integration are

Q: Question 23 en [ "_f(x)dx=0 and ["f(x)dx = 1, evaluate Given A 0 B (u) D 11 76 55 =¹3f(x) dx -…

A: We have to find out the integral

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Q: A B 15 / = √=42+ = ²1 If S (x+1) dx (x+2)(x-1)² + x x-1 1 2 A - 93 2 B C (D) 1 -la - 93 -la I 2 3 2…

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Q: Question 4 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

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Q: Solve the integral: Seln(2x² + 3x − 4)³ (4x + 3) dx

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Q: Let f(x)=√3x-2 on the interval axis and find the volume of the resulting solid. 43л -unit 3 135 83…

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Q: Please write out/show work, thank you! Find the slope of the line tangent to 2xy + π sin y = 2π…

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Q: S sec (x-1) tan4 (x - 1)dx, which of the following equations will be useful for 1 + cos2u cos²u= 2…

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: Solution: Natural length  = 3 ft   ---> 18 ft-lb 3 ft to 6 ft

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

A: We have to find out the option

Q: Why does dA/dt = 0?

A: Since area is constant therefore dA/dt=0

Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

A: Double integration need to be done.

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A: A company has two packaging machines in a unit, each with a different daily capacity. The capacity…

Q: + ∞o [** S The improper integral A B) 1 8 ex dx is

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→dx=-du=-∫euduWe know that ∫audu=auln(a)

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: To evaluate the integral sin ³0cos 0d0 by trigonometric transformation, we use the identity; A…

A: ∫sin3θcos6θ dθ

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x +1. 1 A = unit ² B 3 2…

A: Determine the area bounded by the function f(x)= (x+1)3, g(x)= x+1 .

Q: 9n + 5 5 | 4m3 + 2n? + 5

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

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Q: 1 1 11 f_²_f(x) dx = f(x) dx = 0 and f(x)dx [² f(x) dx = 1 1 ₁ 6' 1 0 [²3F(x) dx - √ 2P(x)dx -1 11 6…

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Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 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: f(x)=√3x-2 on the interval Let of the resulting solid. 83 (A) -unit 3 135 43x B -unit3 125 83x…

A: Ans : A

Q: 21) Write a function that has an infinite discontinuity at x = 100. 22) Write a function that is…

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

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Q: Evaluate the improper integral 3 A 4 B O diverges N|9 름 12²233/30 dx

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Q: I5 = 2 -3 x 0(x - 1)dx

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Q: 6) (-2√√2, 2√2) 8) (2 3 3√3 2' 2 10) (-2,-2√3)

A: