142 Answered Questions for the topic integral calculus

One end of a pool is a verticle wall 16 ft wide.

One end of a pool is a verticle wall 16 ft wide. What is the force exerted on this wall by the water if it is 7 ft deep? The density of water is 62.4 lb/ft^3.

Calculus: Vector Integration

Three paths from (0,0) to (1,2) are defined by (a) y=2x (b) y=2x^2(c) y=0 from (0,0) to (1,0) and x= 1 from (1,0) to (1,2). Sketch each path and along each path find (integral)c Fdr, where F=... more

Consider the region between the graph of f(x)=x−2 and the x-axis on [2,4]. For the line of rotation given below, use a definite integral to find the volume of the resulting solid.

Around the line x=7 The volume of the solid is___________? PLEASE show work!! STEP BY STEP!!!

What are maximum and minimum values of the function (definite integral)

What are maximum and minimum values of the function f(a,b)= ∫_a^b e^(-(x-3)^2 ) dx ?

2 cosx -3 sinx/6cos x + 4 Sin x

Wy cant I take the denominator as t as it is and get the answer, why is it necassary to take 2 common in the denominator.If I suppose t= denominator , then the answer isnt similar to as mentioned... more

What happens when the given integral of a function has domain restrictions.

The integral of cosec x dx is given as ln (cosec x - cot x) yet this function has domain restrictions eg at x = 5. This seems to be the tip of the iceberg on integration. The given integral of... more

Given two equation, find intersect point, enclosed area and need to sketch graph!

Determine each of the following.i. Sketch 𝑦1 and 𝑦2 in the same graph.ii. Shaded the area of the region bounded.iii. Find the intersection points.iv. Find the enclosed area.

Identify the critical points of the function. & Determine the intervals on which the function increases and decreases.

answer each of the following questions.i. Identify the critical points of the function.ii. Determine the intervals on which the function increases and decreases.

Why ∫ 0 to 1 of sin(x) isn't the same as calculating the indefinite integral at x=1?

I thought of this after reading https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#Geometric_meaningIt turns out that the answer is just the difference between the indefinite integral at... more

Integral Question

Suppose that ∫3-1f(x)dx = 4 and ∫35f(x)dx = 1. Find ∫-15 (2f(x) - 3)dxa. -10b. 0c. 3d. 6e. 10f. 12

Which of the following options satisfies y(1)?

Let A(x) and B(x) be functions defined by A(x) = integral (exp(t^2-2t) dt) [upper bound:x lower bound: 0]B(x) = integral (exp(t^2+2t) dt) [upper bound: x lower bound: 0]where t is a dummy variable.... more

Use substitution to find ʃ x(x^2 – 4)^2 dx

Find an integral of function

Find an integral of the function:f(x)= (ln abs(x+7))abs=absolute value

Calculus: Integral Calculus

Evaluate ∫1/(1-cos(x)+sin(x))

Finding centroid

A quarter with the center at the origin and radius of 1 unit is out from a square with side of 1 unit. the square has its lower left corner at the origin. Determine the centroid of the remaining area. more
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