Calculus Integration part 1
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Sin(x)Cos(y) | 1/2(sin(x-y) + sin(x+y))
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| sin(x)sin(y) | 1/2(cos(x-y) - cos(x+y))
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| cos(x)cos(y) | 1/2(cos(x-y) + cos(x+y))
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| sin^2(x) | 1-cos(2x)/2
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| cos^2(x) | 1+cos(2x)/2
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| (a^2-x^2)^1/2 subst? | x=asin(t)
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| Sin(x)Cos(y) | 1/2(sin(x-y) + sin(x+y))
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| (a^2-x^2)^1/2 which identity do you use? | 1-sin^2(t)=cos^2(t)
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| sin(x)sin(y) | 1/2(cos(x-y) - cos(x+y))
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| (a^2+x^2)^1/2 which identity do you use? | 1+tan^2(t)=sec^2(t)
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| cos(x)cos(y) | 1/2(cos(x-y) + cos(x+y))
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| sin^2(x) | 1-cos(2x)/2
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| cos^2(x) | 1+cos(2x)/2
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| (x^2-a^2)^1/2 which identity do you use? | sec^2(t)-1=tan^2(t)
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| (a^2-x^2)^1/2 subst? | x=asin(t)
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| Intergral f'(x)g(x)dx = | f(x)g(x)-integral f(x)g'(x)dx
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| (a^2-x^2)^1/2 which identity do you use? | 1-sin^2(t)=cos^2(t)
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| Shell Method | V=2(pi)rh(dr)
V=(circumference)(height)(thickness)
integral 2(pi)x(f(x))dx
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| (a^2+x^2)^1/2 subst? | x=atan(t)
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| Volumes formula | V=integral A(x)dx
A(x)=area
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| (a^2+x^2)^1/2 which identity do you use? | 1+tan^2(t)=sec^2(t)
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| Washer Method | V=integral (pi)r^2-(pi)r^2dx
V=integral (pi)(outer radius)^2 - (pi)(inner radius)^2 dx
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| (x^2-a^2)^1/2 subst? | x=asec(t)
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| Shell Method choosing variable of integral | Variable of the integral should be in the same direction as the axis of rotation
x=0 is dx
y=0 is dy
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| (x^2-a^2)^1/2 which identity do you use? | sec^2(t)-1=tan^2(t)
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| Washer Method choosing variable of integral | variable of integral should be going the opposite direction of the axis of rotation(but can be either)
x=0 is dy
y=0 is dx
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| Intergral f'(x)g(x)dx = | Intergral f'(x)g(x)dx = f(x)g(x)-integral f(x)g'(x)dx
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| Work = ? | W=fd or W=mgd
work=force*distance
or work=(mass*gravity)*distance
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| Shell Method | V=2(pi)rh(dr)
V=(circumference)(height)(thickness)
integral 2(pi)x(f(x))dx
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| Work = ? (integral) | W=integral f*dx
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| Volumes formula | V=integral A(x)dx
A(x)=area
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| Hook's Law | F=kd
Force=(hook's constant)(distance stretched from natural length)
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| Washer Method | V=integral (pi)r^2-(pi)r^2dx
V=integral (pi)(outer radius)^2 - (pi)(inner radius)^2 dx
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| Work = (integral)(Hook's Law) | W= integral k*x*dx
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| Shell Method choosing variable of integral | Variable of the integral should be in the same direction as the axis of rotation
x=0 is dx
y=0 is dy
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| Average value |
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| Washer Method choosing variable of integral | variable of integral should be going the opposite direction of the axis of rotation(but can be either)
x=0 is dy
y=0 is dx
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| Work = ? | W=fd or W=mgd
work=force*distance
or work=(mass*gravity)*distance
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| Work = ? (integral) | W=integral f*dx
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| Hook's Law | F=kd
Force=(hook's constant)(distance stretched from natural length)
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| Work = (integral)(Hook's Law) | W= integral k*x*dx
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| Average value of a function | 1/(b-a) intergral f(x)dx
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| Work = (pumping) | W=integral (distance)(density)(area)dx
Work=integral (distance cross section will move)(density)(area of cross section)(dx or dy)
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