Question Answer
What does a definite integral find? The area underneath a curve.
What is an alternative use of integrals? Finding the length of a curve.
Who was credited with the first systematic technique for determining integrals? Eudoxus.
Who are the founders of Calculus, in which integrals are one of the techniques that can be categorized within the field? Isaac Newton and Liebniz.
Is there a power rule for integration? No. Power rule only applies to derivatives. U substitution undoes the power rule.
Find the integral of 8x^7 x^8 +C
Find the integral of cos(x) sin(x) +C
Find the integral of 1/(25-4x^2)^(1/2) (((sin2x/5))^(-1))/2 +C
Where are integrals used in the real world? Their applications in statistics, physics(engineering), and other fields make them extremely useful.
Is a riemann sum equivalent to an integral? No. Reimann sums are a cruder version of integrals, typically containing some error in their calculation. Hypothetically, with infinite rectangles, the riemann sum would be equivalent to the integral.
What are riemann sums? Riemann sums are an approximation of the area underneath a curve.
Find the intergral of Cos (x)^4 (12x+8sin(2x)+(sin(4x))/32 +C
Summarize the Mean Value Thereom for integrals. For a continuous function there is a point that equals the average of the function from the two endpoints.
The intergral is the opposite of what mathamatical concept. The derivitive.
True or False Intergrals can be used to find the area under curves in respect to the y-axis as well as the x-axis. True
True or False Some Intergrals do not have a limit. True
True or False the area under a curve will always be given by the value of an intergral False, if the area is below the axix then it is negative and will change the value of the integral.
Find the intergral of 8x^3+3x^2-18x+3 2x^4+3x^3-9x^2+3x +C
What is the formula for the Volume of a curve revolved around an axis. S (R^2)-(r^2) dr (from a to b)
What must you do if you are doing an improper integral? You have to take the limit of some variable, like a,b, or c, and carry out the integration.
How do you tell if an integral is divergent or convergent? When you carry out the integration and substitute variables in the integral is convergent only if terms are 0 over something or something over infinity. If there is 0 over 0 or infinity over infinity this does not meen the curve is convergent.
How does one take the definite integral of an equation that is non differentiable along the interval? Break up the integral into seperate integrals. Then set up a limit where some variable approaches the value of non differentiability.
Who is the sugar daddy of calculus? Bryan Zimmerman
What are possible tests of convergence for determining if an integral converges? Integral test, p test, comparison test, ratio test, and nth value test.
Why was calculus created? To do physics.
What are possible methods for doing solids of revolution? Washer method and hollow cylinder method.
The derivative of the integral of a function is equal to The original function.
True or False the original fuction is representative of the slop of the intergral. True
What is the integral of x^(1/2) (2(x)^(3/2))/3 +c
Calculus is fun no comment
True or false the answear to an integral is always positive. False it can be negative as well.
What is the integral of -cosx -sinx +C

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