204 Answered Questions for the topic integral


How do you find the upper bound of an integral

12000-inte(0 to A) r(t)dt= 9000   r(t)= 600t/t+3 for 0 less than or equal to t less than or equal 5 r(t)= t>5 (Piecewise)  


Assume s,v, and a are continuous functions and s is twice differentiable, where s(t) represents the position, v(t) is velocity, a(t) is acceleration

 Find the following:   d/dx of integral from t to t^2 of v(w)dw   integral from t to t^2 of v(w)dw   second derivative of integral from t to t^2 of v(w)dw    Calculus question I am stuck on


Integral of Sin-1 logx

Sin-1logx find integral 


Stuck on pratice problem reguarding integrals

a. Explain why ∫02pi sin(x)dx = 0   b. Can you set up another integral, or perhaps multiple integrals, to compute the total (unsigned) area between sin(x) and the x-axis on the interval [0,2pi]


plane areas in rectangular coordinates (please help)

Find the area bounded by the curve: y = x(x-1)^2, the line y = 2, and the y - axis
Integral Calculus 3



Set up an iterated integral to evaluate I=R⌠⌠⌠f(x,y,z) dv, where R is the region in the first octant bounded by the surface z=x+y^2, the cylinders y=2sqrt(x), x=2sqrt(y), and the... more


Integration question involving cosh^-1???

Evaluate the integral (1/sqrt(x^2 - 5))dx on limits of 3 to 4, using the formula: integral of (1/sqrt(x^2 - a^2))dx. Recall that this formula was found by using the substitution x = a cosh t, and... more
Integral Calculus


Find an anti-derivative F(x) with F'(x) = f(x) and F(0)=0

Find an anti-derivative F(x) with F'(x) = f(x) and F(0)=0   f(x)=(1/5)x


Evaluate the integral below given R. (Hint: what is the upper boundary of x?)

Evaluate the integral below given R. (Hint: what is the upper boundary of x?)     ∫∫1_R^  xy daR bounded byx=0y=0y=9−x^2      

Find the integral below.

Find the integral below.       ∫∫1_R^ (x+2y) dar={(x, y):0≤x≤3, 1≤y≤4}    
Integral Calculus


Integral of the equation

∫1/(√x√(1-x)) dx
Integral Calculus


How to find this integral?

∫(x+5)/(√9-(x-3)2)   This problem is stumping me! Also the square root is over the whole denominator. 


Cubic curve integral - area enclosing curve and x-axis

The curve is x^3-6x^2+11x-6. I have to prove that the two regions enclosed between the x-axis and the curve are equal. Given is, that the curve cuts the x-axis at x=1,x=2 and x=3. I tried finding... more


solution of indefinite integral

What is a particular solution of the indefinite integral ∫(2)/(1-x2)dx that passes through (√3 , (Π/2)?   a) f(x)=√(3) tan-1x-(Π/6) b) f(x)=2tan-1x-(Π/6) c) f(x)=2tan-1x+√(3)
Integral Math Calculus Ap Calc


substituting in an integral

If the substitution √(X)=sin y is made in the integrand of: (top of the integral sign is (1/2), bottom of the sign is 0) ∫ ( √(X) )/( √(1-X) )dx, the resulting integral is_____________.   A.)... more


chain rule is also know as

The Chain Rule for antiderivatives is also known as the ___________________ rule.   -derivative -substitution -product -integral


integrals for area between curves

what integral formula would represent the area between the curves f(x)=-x2+2x+3 and g(x)=x+1 on the interval [-1,2]?


solving integrals

∫ ( (dx)/√(x2+36) )=_____________     a. ( (√(x2+36)+x)/6 )+C   b. ln abs( (x+6)/(√(x2+36)) )+C   c. ln ( (√(x2+36)+x)/6 )+C      


trigonometric substitution to evaluate integral

Which trigonometric substitution can be used  to evaluate the integral: ∫ ( (dx)/(√(a2+x2)) ) ...?   x= a tanθ   x=a sinθ   x=a secθ


substituting a value into an integrand

if the substitution √(x)=sin(y) is made into the integrand of (with the upper limit of: 1/2  and the lower limit of: 0) ∫ ( (√(x) )/( (√(1-x) )dx , the resulting integral is _______________.    


Area bounded by two curves

What is the area of the region bounded by the curves y=2(x^2)-7 and y=2/x between x=1 and x=3? Please and thank you!


Evaluate the integral

Evaluate the integral  ∫(-9/3√(x-9))dx with upper bound 9 and lower bound 1
Integral Derivative


Find the derivative of

Find the derivative of  g'(x)=∫(u+4/u-5)du with upper bound 3x and lower bound 9x 
Integral Derivative Function


Find the derivative of the following integral

find the derivative of    g(x)= ∫(u+4/u-5)du with upper bound 3x and lower bound 9x g'(x)=?
Integral Calculus


At what value of t does the local max occur?

f(t)= integral (x^2+11x+24)/(1+cos^2(x)) from 0 to t  At what value of t does the local max of f(t) occur?

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