Evaluating 9-x² dx using trigonometric substitution will lead to: A of th (A) cos²0d0 [*/ cos²0de Ⓒ 18 √2/2 57/2 (B) **/2 C sin²0d0

Q: A lighthouse is on an island 400 meters off shore. The lighthouse beam makes a full turn every 15…

A: answer is in next step

Q: Question 36 Evaluate the triple integral: (x+y+z)dydxdz 0 A 24 B) 18 (C) 6 D) 12

A:

Q: tanx If f(x) = (Α) B C D S 0 sec ³x 1+etanx In (secx) √ 1+tan²x tanx 1+e sec²x 1+ etanx 1+1² -dt,…

A: Here, given that: f(x)=∫0tan x1+t21+etdt...(1)

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:

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² − 4 = 0, using a vertical element.…

A:

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: 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…

A:

Q: Determine the area bounded by f(x) = x² - X and x-axis. A -unit² uni B unit² 1 -unit² C D -unit² 2 3…

A:

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

A:

Q: Solve the integral: A 5n/1+x²|+C 5 (B) 6in 5+x' 6In|5+ +C 음 m/1+x²|+c C ³√|+C 1+x √√√√x+x² dx D

A:

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: Integration

Q: x + 2 Determine the case of the following proper rational function after simplification: (x² – 4)(x³…

A: Ans: C

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

A:

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming Ⓒ S A 1-z² B 1+z² © √ 1 +…

A:

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

A: The region bounded by line y = x - 1 and the curve y = (x - 1)3 is as below

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

A:

Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

A:

Q: Evaluate the integral: A B C D H|m 1 6 1 |ო 3 √ sin S 1 6 sin(3x)cos(3x) dx

A:

Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: Evaluate the triple integral: 3 2 1 S³ S² S²(x+y+z)dydxdz 0 A 12 B 18 C 6 D) 24

A:

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

A:

Q: en [_²_f(x) dx = 0 and ² fl Given f(x) dx = 11 6 T evaluate √3f(x)dx- -S__2f(x)dx.

A:

Q: Given A B с D f(x) dx = 0 and [ f(x) dx = 11₁ -1 11 6 55 6 0 11 5 - S²3f(x) dx - √₁2 f(x) dx.…

A:

Q: Given Sf(x) dx = 0 and √ ² f(x) dx = 11 6 " 1 0 •√3f(x) dx - √₁2f(x) dx. evaluate

A:

Q: Evaluate the double integral: S²² (3x² +9y²) dxdy 0

A:

Q: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

A:

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

A:

Q: solve the following differential eqaution : (2x+y)dx-(4x+2y-1)dy=0

A: Solved below.

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

A:

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

A:

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

A:

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

A:

Q: 2 Let f(x)=√√3x-2 on the interval 1. Revolve the region between the curve, y=1 and y-axis about the…

A: To solve this problem we use cylindrical shell.. method.

Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: We have to find out derivative

Q: (x + 1) dx (x+2)(x-1)² 15 S= = √ [ +42 A B + x + 2 x-1 C + + (x-1)2]dx. dx, the values of A & C…

A:

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

A: Let's find volume of solid.

Q: Question 11 If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant,…

A: Topic:- application of integration

Q: Evaluate the improper integral 3 A 4 B) diverges с 0 D 2 N|O √√² 3³/3 m|f dx

A:

Q: 11 Given ~ [²₁_f(x) dx = 0 and [ ² f(x) dx = 1 1 1 4 11 A 6 B C 0 55 0 evaluate • [²³f(x) dx - ²₁²…

A:

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

A:

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

A:

Q: Evaluate

A:

Q: In S₁² = 10 A (1,00) B (-∞0,00) c) (-∞,1] D {0,1} Given -dx, determine all value/values of P for…

A:

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

A:

Q: √ Given A B CO f(x) dx = 0 and 11 55 6 √ √²+ f(x) dx = 1/201₁ 11 6 , evaluate √3 3f(x) dx - ₁2 f(x)…

A: To solve the integration using properties and given data.

Q: Given B ₁ [_²_f(x) dx = 0 and [ f(x) dx = 11 2 55 6 D 0 11 11 = √²3f(x) dx - _2f(x) dx. evaluate

A:

Q: Evaluate the double integral: A B C D m 100 +10 9|N NIG 4 S** 2ydydx 1

A: A detailed solution is given below.

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

A: consider9x2+6x-7=9x2+6x+9-16=9(x+3)2-16 let u=x+3⇒du=dxThen9(x+3)2-16=9u2-16

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

A: topic- indefinite integral

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

A: ∫sin3θcos6θ dθ