Integrate
Usubstitution
Harder Usubstitution
Basic Questions
Random facts
100
∫cos(x)dx
sin(x)
100
Find U and DU: ∫√(3x-1)dx
U: 3x-1 DU: 3dx
100
The incorrect equation is:
A. The Integral of sin(x) dx equals -cos(x)
B. The Integral of cos(x) dx equals sin(x)
C. The Integral of csc^2(x) dx equals cot(x)
D. The Integral of sec^2(x) dx equals tan(x)
E. All of the Above
E, All of the Above
Remember +C
100
What are integrals used to solve?
The area under the graph
100
What color are zebras?
Black with white stripes.
200
∫(x2 + 2x - 3) / (x4) dx
-1/x - 1/x2 + 1/x3 +
200
∫4x³(x⁴-7)⁵ dx
1/6(x⁴-7)⁶ + C
200
∫ cos³(x)∙sin(x) dx
-1/4(cosx)⁴+ C
200
You complete an antiderivative by adding this to the end of the equation
+C
200
True or False: Is a poptart a ravioli?
True
300
∫7/x2 dx
-7/x+C
300
∫4x³ / (x⁴+5)³ dx
-1/2(x⁴+5)^-2 + C
300
∫sec³x∙tanx dx
1/3sec³x + C
300
What is this called
Fundamental Theorem of Calculus
300
What country has did Mrs. Duncan visit as a 13 year old (without her parents)? She heard people playing a didgeridoo,
Australia
400
∫(x + 1)(3x - 2) dx
x3 + (1/2 x2) - 2x + C
400
∫3x⁵ √(x⁶-4) dx
1/3(x⁶-4)^(3/2) + C
400
∫sin²(3x)cos²(3x)dx
1/9sin³3x+C
400
The process of finding the rate of change of a function at an exact moment is called this.
Derivative
400
What does the acronym DNA stand for?
Deoxyribonucleic acid
500
∫(4x3 + 6x2 - 1) dx
x4+ 2x3 - x + C
500
∫ (x^2 + 2x - 3) / (x^4)
(2t - 1)^2 dt
4/3 t3 - 2t2 + t + C
500
∫sec2 (5x + 1) dx
1/5 tan(5x + 1) + C
500
The second derivative indicates...
a. velocity
b. acceleration
c. the derivative of the integral
d. integral
b. acceleration
500
What are the four houses at Hogwarts School of Witchcraft and Wizardry?
Gryffindor, Ravenclaw, Hufflepuff, & Slytherin