Question

In: Math

Evaluate the integral: ∫√36x^2−49 / x^3 dx (A) Which trig substitution is correct for this integral?...

Evaluate the integral: ∫√36x^2−49 / x^3 dx

(A) Which trig substitution is correct for this integral?

x=49/36sec(θ)
x=7/6sec(θ)
x=1/36sec(θ)
x=6/7sec(θ)
x=7/6sin(θ)

(B) Which integral do you obtain after substituting for xx?
Note: to enter θθ, type the word theta.

(C) What is the value of the above integral in terms of θ?

(D) What is the value of the original integral in terms of x?

Note: WAMAP does not recognize the inverse secant (arcsec) function. You will need to use another inverse trig function when you fill in your answer below.

Expert Solution

Let

B)

C)

D)

milcah answered 1 year ago

Evaluate the integral: ∫−14 / x^2√x^2+100 dx (A) Which trig substitution is correct for this integral?...

Evaluate the integral: ∫−14 / x^2√x^2+100 dx (A) Which trig substitution is correct for this integral? x=−14sec(θ) x=100sec(θ) x=10tan(θ) x=100sin(θ) x=10sin(θ) x=100tan(θ) (B) Which integral do you obtain after substituting for x and simplifying? Note: to enter θ, type the word theta. (C) What is the value of the above integral in terms of θ? (D) What is the value of the original integral in terms of x?

Evaluate each integral using trig substitutions 1.) Integral of (3x^5dx)/(sqrt(16-x^2) 2.) Integral of (sqrt(x^2-16)dx)/x 3.) Integral...

Evaluate each integral using trig substitutions 1.) Integral of (3x^5dx)/(sqrt(16-x^2) 2.) Integral of (sqrt(x^2-16)dx)/x 3.) Integral of (6dx)/(16+16x^2)

Evaluate the integral (x^3+2x^2-4x+5)/(3x^2+x-10)dx

Evaluate the integral. ∫4−2. (1/(x+5)((x^2)+16)) dx

Evaluate the integral. (Use C for the constant of integration.) (x^2-1)/(sqrt(25+x^2)*dx Evaluate the integral. (Use C...

Evaluate the integral. (Use C for the constant of integration.) (x^2-1)/(sqrt(25+x^2)*dx Evaluate the integral. (Use C for the constant of integration.) dx/sqrt(9x^2-16)^3 Evaluate the integral. (Use C for the constant of integration.) 3/(x(x+2)(3x-1))*dx

integration of ((8(x+a))/(x^2+a^2))dx. using trig. sub.

1. evaluate ∫ 8sec^3(2x)dx. Perform the substitution u= ∫ 8sec3(2x)dx= ? +c 2. evaluate ∫...

1. evaluate ∫ 8sec^3(2x)dx. Perform the substitution u= ∫ 8sec3(2x)dx= ? +c 2. evaluate ∫ sqrt(e^8x-36)dx Perform the substitution u= ∫ sqrt(e^8x-36)dx= ? +c 3. evaluate ∫ e^x / (16-e^2x)dx Perform the substitution u= ∫ e^x / (16-e^2x)dx = ? +c 4. evaluate ∫cos^4(7x)dx. Perform the substitution u= ∫cos^4(7x)dx= ? +c

evaluate the indefinite integral. ∫10x2−49x+21/(x−3)(x2−2x−3)dx

1. (a) Evaluate the integral: ∫0 to 2 16 /x^2+4 dx Your answer should be in...

1. (a) Evaluate the integral: ∫0 to 2 16 /x^2+4 dx Your answer should be in the form kπkπ, where k is an integer. What is the value of k? Hint: d/dx arctan(x)=1/x^2+1 k= (b) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use the alternating series estimation.) = 2. The function f(x)=8xln(1+x) is represented as a power series f(x)=∞∑n=0 cn x^n. Find the specified coefficients in the power series....

Integral x^5-x^4+4x^3-4x^2+8x-4 / ( x^3+2)^3(x^2-1) dx