C-faring
Integrate ∫(4x^2+x+3)dx
What is 4/3x^3+x^2/2+3x+C
Use the Fundamental Theorem of Calculus to evaluate ∫(3+x)dx on [0,8]
What is 56
Integrate ∫[x^2/(sqrt(x^3+3))]dx
What is 2/3 sqrt(x^3+3)+C
Evaluate the sum from i = 1 to 5
Σ (5i + 2)
85
Find the average value of f(x)=x^3 over the interval [0,2].
2
Integrate ∫(2x - 9 sinx )dx
What is x^2 + 9cosx+C
Use the Fundamental Theorem of Calculus to evaluate ∫(4x^3-2x)dx on [-1,1].
What is 0
Integrate ∫[x(1-3x^2)^4]dx
What is (-1/30)(1-3x^2)^5 +C
Calculate R4 for f(x) = 2x + 5 on the interval [0,2].
15
Use the Fundamental Theorem of Calculus to evaluate ∫sin(2x) dx on [-pi/4,pi/4]
0
Integrate
∫ (x - sqrt(x) dx
x^2/2 - 2 x^(3/2)/3 + C
Use the Fundamental Theorem of Calculus to evaluate ∫(x√x) dx on [4,9].
What is 422/5
Integrate ∫[(sinx)^3cosx]dx
What is (1/4)(sinx)^4+C
Calculate L4 for f(x) = x^2 over [0,3].
363/64
Find the value(s) of c guaranteed by the Mean Value Theorem.
f(x)=sqrt(x) over the interval [4,9].
c = (38/15)^2 = 1444/225
∫(Θ2 + sec2 Θ) dΘ
Θ3/3 + tan Θ + C
Use the Fundamental Theorem of Calculus to evaluate ∫x(x^2-6)dx on [-2,1]
What is 21/4
Integrate ∫xsqrt(x+5)dx
(2/5)(x+5)^(5/2)-(10/3)(x+5)^(3/2)+C
Calculate M4 for f(x) = x^2 + 4x on [0, 4]
53
The velocity of a particle is given by
v(t) = 5t - 10 in meters per second.
Find the total distance traveled by the particle on the interval [0,3].
12.5 meters
∫ (tan2 y + 1) dy
tan y + C
Use the Fundamental Theorem of Calculus to evaluate ∫ cos(x/2) dx on [0,pi]
2
∫ csc2(x) / cot3(x) dx
1/2*tan^2(x) + c
The Trapezoidal approximation using n trapezoids is calculated by:
(b-a)/2n * ( f(x_0) + 2*f(x_1) + 2*f(x_2) + ... + 2*f(x_n-1) + f(x_n))
Find T4 for f(x) = sin(x) on the interval [0,pi].
pi(1+sqrt(2))/4
approx 1.896
Find F'(x) for
F(x) = ∫ (from 2 to x^2) 1/t^2 dt
1/x^4 * 2x
2/x^3