Unit 7

Question 1

What is key to remember when integrating or anti deriving?

Answer 1

ALWAYS PUT “+ c” AT THE END

Question 2

How do you integrate with power rule?

Answer 2

Say you’re given 2x^2
2 ( x^2+1 / 2+1)
2/3x^3 + c

Question 3

How do you integrate with 1/x?

Answer 3

S (1/x)dx = ln |x| + c

Question 4

How do you integrate exponential functions?

Answer 4

S (a^f(x) f’(x)dx = (a^f(x))/ lna + c

Question 5

What is the anti derivative of e^mx+b?

Answer 5

S (e^mx+b)dx= a^mx+b / m(lna) + c

Question 6

What is the anti derivative of 1/mx+b?

Answer 6

S (1/mx+b)dx= ln|mx+b|/m

Question 7

What is the anti derivative of sinx?
Cosx?
Tanx?

Answer 7

Sinxdx= -cosx +c
Cosxdx= sinx +c
Tanxdx= -ln|cosx| + c

Question 8

What is the anti derivative of cscx?
Secx?
Cotx?

Answer 8

Cscxdx= ln|cscx-cotx| + c
Secxdx= ln|secx+tanx| +c
Cotxdx= ln|sinx| +c

Question 9

What is the anti derivative of sec2(x)?

Csc2(x)?

Answer 9

Sec2(x)dx= tanx + c
Csc2(x)dx= -cotx + c

Question 10

What is the anti derivative of secxtanx?

Cscxcotx?

Answer 10

Secxtanxdx= secx +c
Cscxcotxdx= -cscx+ c

Question 11

How do we integrate with the chain rule present?

Answer 11

If you have S (f’(g(x)) g’(x)dx then you pick g(x) as u and derive it in terms of u
du = g’(x)dx
Then replace that in the equation

Always pick more complex equation and simply before deriving

Question 12

How do you solve definite integrals?

Answer 12

b b
S (f’(x)dx) = [f(x)]
a a

= f(b) - f(a)

Don’t need to add c because they cancel

Question 13

What does the answer of a definite integral mean?

Answer 13

It is the area between y=f(x) and the x-axis between a and b

Question 14

How do you solve a definite integral using chain rule?

Answer 14

S f’(g(x))g’(x)dx = f’(u)du
= f(u) and change the number by the S to g(a) and g(b)
F(g(b)) - f(g(a))

Question 15

What is the formula to finding the area between two curves?

Answer 15

b
Area= S(upper curve-lower
a curve)dx

Question 16

How do you solve a question that asked to find the area between two curves?

Answer 16

First find the intersection points of the two lines by making them equal to eachother
Then sketch a rough graph of the two
Then find the areas you need to find and input the numbers into the formula

Question 17

What is the formula for integration by points?

Answer 17

Using the product rule
d(uv)=vdu+udv

S(udv)=uv-S(vdu)

Question 18

How do you solve integration by points questions?

Answer 18

First pick a u and a dv from the given integration function
Then find the derivative of u and the integral of dv
Then input all numbers into the equation and simplify

Question 19

What is the one thing to remember when integrating?

Answer 19

ADD C ON THE END

Constant