129 Answered Questions for the topic Integrals

Integrals Antiderivative

11/18/15

what is the antiderivative: 3e^x + 7sec^2x
this problem has to do with anti derivatives and integrals. please help
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08/31/15

Evaluate each of the following integrals.
       2 1)  ∫ 4x dx           3 2)  ∫ (x2+3x)dx          4 3) ∫ (x2-4x+5)dx
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Integrals Math Calculus Ap Calc

08/23/15

True or false. If true, why? If false, what is a counter example, and can you explain why it contradicts? Please
If f and g are differentiable and f(x)≤ g(x) on [a,b], then f'(x)≤g'(x) on [a,b]
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Integrals Math Calculus Function

08/23/15

True or false. If true, why? If false, what is a counter example, and can you explain why it contradicts? Please
If f and g continuous function on [a,b] then (upper: b, lower a)∫f(x)g(x)dx=[(upper: b, lower a)∫f(x)dx]*[(upper: b, lower a)∫g(x)dx].
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Integrals Math Calculus Ap Calc

08/23/15

True or false. If true, why? If false, what is a counter example, and can you explain why it contradicts? Please
If F(x)= (upper: x, lower: 0) ∫√(t3+1)dt  then  F'(2)=3
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Integrals Math Calculus Ap Calc

08/16/15

is this expression correct?
∫ecosxdx=e-sinx+C    
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Integrals Math Calculus Ap Calc

08/16/15

which of the following integrals is INCORRECT?...
A) ∫tanxdx=sec2x+C   B) ∫cscxdx=ln[cscx-cotx]+C   C) ∫cotxdx=ln[sinx]+C  
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08/16/15

integrating
when integrating ∫sin3xdx, a good first move would be to:   a) use u-substitution, letting u=sinx, and then integrating ∫u3du   b) use u-substitution, letting u=sin2x   c) rewrite the problem... more
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08/16/15

dividing definite integrals
∫(top: b, bottom: a) ∫(f(x)/g(x))dx=(top: b, bottom: a)∫f(x)dx÷(top: b, bottom: a)∫g(x)dx   true or false?
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08/16/15

definite integral
which of the following expressions are true about the definite integral of sinx on the interval [0,2Π]?   A) (top 2Π, bottom 0) ∫sinxdx= (Π →∞)lim (top: Π, bottom: i=0)∑sinxi 2Π   B) (top 2Π,... more
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Integrals Math Calculus Ap Calc

08/16/15

true or false?
if f(x) is an even function, (above integral sign: 0  below integral sign: -a) ∫f(x)dx= (above integral sign: a  below integral sign: 0) -∫f(x)dx   true or false?
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08/12/15

solving integrals
∫( (du)/(u(u2-1)1/2) ) = __________________
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08/12/15

solving using integrals
if I have a graph of f(x) and I want to find (on the top of the integral sign is 5, and on the bottom is -2)  ∫f(x)dx   what would ∫f(x)dx equal?... (if the graph has points at (-5,2) (-2,0)... more
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08/12/15

solving integrals
∫ ( (x+3)/√(1-x2) )dx=_____________
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08/11/15

Word problem using rate of change and integrals
A giant spherical snowball is melting such that its radius decreases at a rate of 5 mm per hour. How fast is the surface area changing when the diameter is two meters? How fast is the volume... more
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Integrals Calculus

07/21/15

Calc word problem! Distance and velocity with integrals.
  A particle is released. Its speed t seconds after release is given by v(t)=0.3t^2+8t. How far does the particle travel during the first 4 seconds? How far does the particle travel during the... more
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07/17/15

Express limit as definite integral?
limit as n goes to infinity.   n Σ     i4/n5     on interval [0,1] i=1   Options are:  1             1              1            7          1 ∫  1/x5  , ∫  1/x4    , ∫  x4   ,   ∫  x5  ... more
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Integrals Calculus 1

04/27/15

Consider an integrable function f(x) that is odd
Assume that integral from 0 to 5 f(x)dx=6 and integral from 0 to 8 f(x)dx=4   Find: -integral from 5 to 8 f(x)dx -integral from -5 to 8 f(x)dx                         Please Help!!
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03/23/15

calculate the integral (2x - 4x3) dx
Can you help me calculate the integral ∫²1 (2x - 4x3) dx ?And show me the steps to get there? Thanks!
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12/14/14

How to find the area under multiple curves
I have a problem here that involves three equations. It wants to know the total area that is bounded by these three equations. they are as follows: y=x y=7 y=x2/28 The domain is [0,14] I know... more
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12/14/14

How to find total area of a region
We have a parabola whose formula is y=5sin^2x and is bounded at the top by the line y=5. It is shaded under the y=5 line between x=pi/2 and x=3pi/2. How do I find the area of this shaded... more
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12/02/14

Evaluate the double integral for the function f(x,y) and the given region R.
f(x, y) = 6xy4; R is the rectangle defined by 2 x 3 and -3 y -2
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12/02/14

Evaluate the double integral for the function f(x,y) and the given region R.
f(x, y) = 5y + 3x; R is the rectangle defined by 3 x 4 and 3 y 5
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Integrals Calculus 1

11/26/14

Integral Question
Let ∫[−4.5 to −9] f(x) dx= 5, ∫ [−7.5 to −9] f(x) dx= 2, ∫[−4.5 to −6] f(x) dx= 4. Find ∫[−6 to −7.5] f(x) dx= and ∫ [−7.5 to −6] 5 * f(x) −2 dx= I found out that ∫[−6 to −7.5] f(x) dx= -1 however... more
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Integrals

11/20/14

Integral Help
Evaluate the integral. Assume that A is a real number and that A < 0.   integrate 8/(x-2)^4 from 0 to A
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