Consider the indefinite integral dx: + 8)°

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: calculate the integral in terms of the inverse hyperbolic functions.

A: We know that

Q: Evaluate iterated integral.

A: Given, ∫12∫121xdx dx

Q: Evaluate the iterated integral. 5 sin(x + 6y) dy dx

A:

Q: Evaluate the triple iterated integral. xyz³ dx dy dz

A: ∫02∫02∫-14xyz3dxdydz=∫02∫02x2yz32x=-1x=4dydz…

Q: Express the iterated integral in the opposite order. dy dx

A: First option is the correct option. Find the region of the integration graphically. The value for y…

Q: Find the indefinite integral.

A:

Q: Show that integral - infinity  to infinity  x dx is divergent.

A: We will evaluate the limit of the integral using two different routes and see if we get the same…

Q: Evaluate the integral. inegral (5x +1 )/(2x +1 ) (x-1 ) dx

A:

Q: use a geometry formula to find the exact value of the definite integral (-2x+4)dx on the interval…

A: To evaluate the definite integral from suitable geometric formula , (without using integration)

Q: ( (x? + 1)e* dx

A: Given

Q: Evaluate iterated integral.

A: We have  I=∫34∫126x5+yx dx dy   Integrate with respect to x. We get I=∫346x25×2+ylnx12…

Q: Evaluate iterated integral.

A: Given, ∫01 ∫36 xx2+3y dx dy

Q: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

Q: use a geometry formula to find the exact value of the definite integral  lxl dx on the interval…

A: Line AOC represents the graph of y=mod x in interval [-2,1]. Here coordinates of 0 are (0,0), A are…

Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: dx dy y? 0,

A:

Q: Evaluate the iterated integral. 5 (ху) dy dx

A: Topic = Integration

Q: -1 tan 2y dy

A:

Q: Determine the exact value of the multiple integral -In 101 ex-y+z dx dy dz – In z JIn 99

A:

Q: Evaluate the double integral : 8. dy dx 88 -

A: We have to evaluate the given double integral   The given expression is

Q: Use any method to evaluate the integral. 8 dx (16x? + 1)?

A:

Q: Evaluate the indefinite integral: (8e" + 5 sec? u) du =| + C.

A: We use integration of eu=eu and integration of sec2u= tanu .

Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: S sec?(5x+8) dx=?

A: The objective is to evaluate the integral.

Q: sketch, reverse and evaluate the integral dy dz 15

A:

Q: Evaluate the donble integral dy dx

A:

Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxy dydx

A: We have to integrate the double integral:

Q: Evaluate the integral, if it exists: +z sinx dx z-

A: We will evaluate the integral if it exists in the following step.

Q: Calculate the iterated integral. 12 2ex + 3y dx dy

A: Consider the inner integral, name it as I1 Take the constant 2 out of the integral sign.

Q: Calculate the integral approximations Tb and Mb for sec x dx %3D

A:

Q: Evaluate the indefinite integral.   ∫ Sec3t  tan 3 t dt

A:

Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: Evaluate the integral: + 6 dx = %3D

A: Find the integral by using substitution method

Q: Sketch and evaluate the reverse integral 3. dy dz

A:

Q: Evaluate the integral

A: The integral is given by,

Q: The value of integral .dz is (z – 1)?

A:

Q: the double integral dy dx Evaluate 2.

A:

Q: The integral csc(0.5) dx is equal to

A:

Q: Evaluate the integral. integral 0  to pie /2    cos x + sin x dx

A:

Q: Calculate the integral approximation Sg for 5 dx.

A: Given: ∫-105-x2dx

Q: evaluate the defmite Integral га (X -2)dx 4.

A: Given integral:

Q: Evaluate the indefinite integral: (3e" + 6 sec? u) du: |+ C.

A: As per guide line we have

Q: Evaluate the integral. integral   sec 6  t  / tan 3t dt

A:

Q: sketch, reverse and evaluate the integral dy dx

A:

Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

A:

Q: Evaluate the iterated integral. '5 2ye-* dy dx

A: We have to evaluate given iterated integral.

Q: Evaluate the triple iterated integral. ,3 xyz dx dy dz

A: