Using a trigonometric substitution, the integral /- (9+x²)3/2 dx becomes:

Q: Evaluate integral using trigonometric substitution.

A:

Q: Use trigonometric substitution to find or evaluate the integral.

A: Given: The integral, ∫-12x24-x2dx.

Q: Find the integral. er sin(5x)dx - IT

A: Known integral formula:

Q: sin° (3x) cos“ (3x)dx 4

A: The given integral is ∫sin53xcos43xdx.

Q: Use trigonometric substitution to find or evaluate the integral.

A: Substitute and differentiate the function to find the total differential.

Q: Using an appropriate substitution, the integral cosxe+2 sinx) dx is equal to:

A: Solve intregal

Q: Evaluate the integral sin^3(2x) dx.

A:

Q: 23 dx V25 – x2

A: We integrate the function using trigonometry substitution.

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral.…

A: By applying  trigonometric substitution

Q: The trigonometric integral fs sec² x (tan³ x - 2 tan7 x) dx is equal to

A:

Q: Using appropriate substitution, the integral S ex3 dx is equal to: X4

A: Indefinite integral

Q: After choosing the appropriate trigonometric substitution the integral -dx, becomes

A:

Q: Evaluate the definite integral: 7 dx 3

A: To evaluate the following definite integral.∫347 dx

Q: compute the definite integral.

A:

Q: Find the trigonometric integral. (Use C for the constant of integration.) (cos(20))(sin(0) +…

A:

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

A:

Q: x° cos 2x dx

A:

Q: Use trigonometric substitution to find or evaluate the integral                      ∫√(x2 − 9) / x…

A: Integration: ∫x2-9xdxsubstitute, x2-9=z              xx2-9dx=dz                   dx=x2-9xdz…

Q: Find the trigonometric integral ∫x tan4 x2 dx

A: Given: I=∫xtan4x2dx for evaluating given integral, we substitute  x2=t…

Q: Use a suitable substitution to find the indefinite integral S csc(sin 0) · cos(0)d0

A:

Q: Evaluate the integral 5x sin (x2) dx by using any methods.

A:

Q: Find the indefinite integral f Vx2 – 6x + 5 dx using an appropriate trigonometric substitution.

A:

Q: Evaluate the integral sin'7 x cos x dx

A:

Q: Evaluate the integral.  integral sin 9  x cos 5x dx

A: Given :           ∫ sin9 xcos5 xdx

Q: Use an appropriate trigonometric substitution to evaluate the integral below. x2 dx 9 – x2

A:

Q: /1 x² dx /2 2 x2

A: I am going to calculate this integral using trigonometric substitution.

Q: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

Q: 6x° /9 – x² dx, x = 3 sin(0)

A: Here we have to find the given integration by using the given trigonometric function.

Q: Evaluate the definite integral. 8 dx 1

A:

Q: 2. (x²-1)3/2 - dx

A: Given:      ∫x2-13/2xdx    substitute u=x2-1→dudx=xx2-1→dx=x2-1xdu          =∫u4u2+1du     Perform…

Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

A:

Q: Evaluate integral of {1/(x^2-9)^(3/2)} dx  Using trigonometric substitution

A:

Q: Use trigonometric substitution to find or evaluate the integral

A: the given integral is: ∫34x3x2-9dx we have to use the trigonometric substitution to find or evaluate…

Q: Given the integral sin(3x + 5) dx cos(3x + 5)

A:

Q: Find the trigonometric integral ∫sin x cos4 x dx

A: Consider the integrals: ∫sinx·cos4xdx…

Q: Use trigonometric substitution to find or evaluate the integral                            ∫ x3 /…

A: Consider the given integration as∫x34+x2dx

Q: Integrate | VE 1-4x² dx using a trigonometric substitution.

A:

Q: Evaluate the definite integral. 7 dx 1

A:

Q: Use trigonometric substitution to find or evaluate the integral ∫√(25 − 9x2 )dx

A: Use trigonometric substitution to find or evaluate the integral ∫√(25 − 9x2 )dx

Q: Evaluate the integral.  integral sin 3  x cos 2 x dx

A:

Q: Find the trigonometric integral ∫sin2(x/2)  dx

A: From the given data:

Q: Use trigonometric substitution to solve the integral Jx*V1+x² dx

A: Note the results :     (Identity)

Q: Find the integral using an appropriate trigonometric substitution 25x2 – 1 dx

A:

Q: Evaluate the integral.  integral sin 9  x  dx

A: Given ∫sin9xdx

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: Given query is to find the integral.

Q: Use appropriate substitution and then a trigonometric substitution to evaluate the integral. dx for…

A: The given integral is ∫dxxx2-4. First, use the substitution x=2t. Then, dx=2dt. Substitute the…

Q: Evaluate the integral. 6 sin -1 x dx

A: Given problem:- ∫ 6sin-1(x) dx

Q: Evaluate the definite integral.

A: The given integral is, ∫0214-x2dx The objective is to solve the integral.

Q: (x² sin(x')dx = 3 %3D

A: Given : Integration of X2sin(X3)dx

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.