What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy² 2x³y5-3x²=C D 4x³y² +3x²= Cy4

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

A: Solve by integration

Q: Which of the following is NOT a method for finding volume of solids of revolution? (A) shell method…

A:

Q: To reduce the DE (x+2y-4)dx-(2x+y-5)dy=0 to a DE with homogeneous coefficients, use the…

A: solution:-x+2y-4dx-2x+y-5dy=0dydx=x+2y-42x+y-5the system of linear equation…

Q: the 2) Find the standard deviation of sample. population 2, 4, 7, 12, 15 Find the variance for the…

A: We have to find the variance and standard deviation.

Q: Transforming dx using miscellaneous substitution will yield to secx + 1

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

A:

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…

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

A:

Q: Evaluate the triple integral: A) 12 B) 6 C) 24 D) 18 3 2 1 (x+y+z)dydxdz

A: We have to choose correct option

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

A:

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

A: The correct answer is option (c).

Q: Evaluate the triple integral: A) 6 B) 18 C) 24 D) 12 3 2 1 ²³√ [²√ √ 0 (x+y+z)dydxdz

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

A:

Q: Determine the integral: [x²cosxdx

A:

Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…

A:

Q: That statement "We can use the General Power Formula of Integration for indefinite integrals…

A: Find:when we can use power formula

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: Which of the following represents the volume of the solid generated by revolving the region bounded…

A:

Q: Which of the following can be determined given Ⓒ [² (4f(x) + 9h(x)) dx 3 ® √²³((x) + B © ²(f(x) -…

A:

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

A:

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

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Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3.

A:

Q: Given the integral sec (x - 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: Let's find useful formula for evaluation of integration.

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

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Q: Evaluate the given definite integral [ 2x³ – 6x² dx, from x = 1 to x = 2 X²

A:

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

A: According to the properties of definite integral(A) ∫abkf(x)dx=k∫abf(x)dx      True(B)∫abkdx=k…

Q: S₁² = P² 1 хо A (-∞,1] B {0,1} с (1,00) D (-∞0,00) Given dx, determine all value/values of P for…

A: Here we have to determine all values of p in which the given improper integral is converges.

Q: Determine the area bounded by the functions f(x) = (x + 1)3³ and g(x)=x+1₁ A unit² B unit² 3 Ⓒunit²…

A:

Q: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

Q: etermine the area bounded by f(x)=x²-x and x-axis. 1 A unit² 2 B unit² 1 unit² 1 unit² D

A:

Q: Evaluate the integral: Sen(1²2+3x-7) е dx A x² + 5x+In 3x-6|+C XZ B +5x+31n|x-2|+C 2 C x ²2+ = +…

A: On solving this we will get

Q: =√x, x=4 and the x-axis, the limits of integration are: If a horizontal element is used to find the…

A:

Q: Determine the area bounded by f(x) = x² — X and x-axis. 1 A -unit² B -unit² Ⓒunit² 2 Ⓒ -unit² 1

A:

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and 1 A -unit² 3 B -unit² 3 -unit² 4 1…

A:

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

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: 3 1 Evaluate the triple integral: f(x+y+z)dydxdz S (A) 24 (B) 12 C) 6 (D) 18

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: Evaluate the double integral: 2 √ ² √² (3x² +9y²) dx dy 0

A: To solve the given double integral.

Q: Question 33 If g(x)=- A) B D d = 2√²-1 (2 ·S^*^[e'-In(21+1)]dt, find g''(x) - 4 (2x+ (2x + 1)² e*…

A: Solved below.

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

A: To find integrand the steps are as follows.

Q: For the given cost function C(x) = 72900 + 800x + x², First, find the average cost function. Use it…

A:

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

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

A: B option is correct.

Q: ·S A B If D A (x+2)(x-1)² = √2 + x + 1 2 9 3 9 -la 1 I 2 93 1 9 2 9 3 . 2|3 B x-1 + C (x-1)2 (x -…

A:

Q: Given the integral [sec (x - 1) tan4 (x − 1)dx, which of the following equations will be useful for…

A:

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming A B © ² с -dz 1+z² © S²+ /…

A: Please see the answer below.