Evaluate the integral: e³+cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 2In3 + C (3e)3+ sinh2x B 2 + In3 (3e)3+cosh2x 2+2ln3 (3e)3+cosh2x 21n3 D + C - + C - + C

Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

Q: B $S₁ (x+2)(x-1)² = √[=42+²1+ (-₁2). (x 1)² ]dx, 1 x-1 A B C If -io 9 -ja -ia 2/3 1 2|3 2/3 2 the…

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: How many antiderivatives does a function of the form f(x)=x" have when n0? (A) none (B) may vary…

A: solution

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: A detailed solution is given below

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

A: Integration

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

A: The given expression is:…

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

A: Double Integration by iteration:

Q: Question 12 Given S (A) (-∞0,00) B (1,00) D -dx, determine all value/values of P for which the…

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

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

A:

Q: e integral: J √√√x+x F1+x X + C 1 x C 5 + C 6in|5+ x² +C 6

A:

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

A: Intergrand

Q: S ³f(x) dx = 5, ³g(x) dx = 7, and Which of the following can be determined given Ⓒ S (f(x) - g(x))…

A: We have to solve integral

Q: ral: Seln(2x²+3x-4)³ (4x+3)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: In the indefinite Integral in(cosh x + e*)- A sinh xte cosh x + ex sinh x + ex In(cosh x + e*)…

A:

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

A: answer is in next step

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x +1.

A: Correct option is A

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

A: We need to find volume.

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

A:

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

A:

Q: X √√/31/22 Solve the integral: 3√/x² A + C 6 B 6√√√x + C C3√√√x² + C C) dx

A:

Q: Given the integral csc²u=cot²u+1 1+ cos2u 2 1-cos2u 2 sec²u=1+tan²u B cos²u=- sec (x-1) tan4…

A: According to our guidelines we can answer only one question or three subparts of a question. Other…

Q: Determine the case of the following proper rational function after simplification: X+2 (x²-4)(x³-8)…

A: Correct option is missing

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

A: The integration are.  .

Q: Evaluate the improper integral A 0 B (C) 2 9 mit 3 4 √1²23 3³/30 D) diverges dx

A:

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

A:

Q: Evaluate: A B С) D (x+1) log(x+1) 1 -In[log(x+1)] + C In 10 1 -In 10 log² (x + 1) + C 2 In 10…

A: Given problem:-

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…

A:

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

A: Solve it

Q: πT Evaluate the integral: S sin(3x)cos(3x) dx

A: We can solve this as follows:

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

A: A option is correct.

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, th (A) 0 and…

A: Topic:- application of integration

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

A:

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

A: Given that g(x) is a differentiable function and range of g(x) is interval I. f(x) is a function…

Q: πT Evaluate the integral: sin(3x)cos(3x) dx រ 1 A 3 (B) i D 1 براس 1

A:

Q: Question 10 tanx If f(x)= A (B) C D sec ³x Itelin sec²x Iteline 1+1² I+e' -dt, then f'(x) equals…

A:

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

A:

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

A: Option (B) is the correct answer.

Q: Question 1 S A - -/-/- B If (0 dx (0+2)(x-1)² 12 93 -ja 12 3 - I 3 B -S[ = √( 14+2+ = -1 (1-12 4 +…

A: We can solve this as follows:

Q: A solid is formed by rotating the area between the curves y = x and y = x² between x = 0 and x = 1…

A: To solve this problem we use washer method.

Q: Stan² √I+1² 0 l+e' 1+tan²x tanx 1+e In (secx)√1+tan²x 1+et tanx sec²x 1+elanx sec 3x If f(x) = A B…

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

Q: Evaluating A 18 √*1/200 (A) **/2 B √9-x² dx using trigonometric substitution will lead to: cos²0d0 0…

A:

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

A: integration

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: + ∞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: Transforming S Ⓒ / ² A 1-z² 1+z² ® / 12-2 B 1+z² © Ⓒ S ²¹²+² dz 1-z2 1+z² D S 1-z² dx secx + 1 -dz -…

A:

Q: Given A) B (C) D 11 √ √ ² f(x) dx = = /10 f(x) dx = 0 and 11 6 20 55 •[ 37/(x)dx - 5² 2/(x)dx…

A: D option is correct.

Q: The improper integral A) 0 B 1 C D) e 8 ·+∞o Ste ex dx is

A:

Q: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

A: