DEFINITE INTEGRATION
CALCULUS

Approximating Area Under A Curve, Area Under a Curve by Limit of Sums, Riemann Sum Tables, First Fundamental Theorem of Calculus, Substitution for Definite Integrals, Mean Value Theorem for Integrals, Second Fundamental Theorem of Calculus

All of our 75 video lessons are numbered below within their corresponding section. Select the section title to be brought to a compilation video lesson of that section. All of these videos are linked to our YouTube Channel. Enjoy!

APPROXIMATING AREA UNDER A CURVE

1. y=(x^2/2)+x+2; [-5, 3]

2. y=x^2+3; [-3, 1]

3. y=-(x^2/2)+6; [-3, 2]

4. y=-(x^2/2)+x+5; [-1, 4]

5. y=-x+5; [-7, -5]

6. y=2/x; [1, 5]

7. y=-x^2+2x+11; [-1, 3]

8. y=x^2-2x+3; [-1, 3]

AREA UNDER A CURVE USING LIMITS OF SUMS

1. ∑ from k=1 to n of 18k

2. ∑ from k=1 to n of (2k+5)

3. ∑ from k=1 to n of 8k^2

4. ∑ from k=1 to n of (k^2+4)

5. lim as n->∞ ∑ from k=1 to n of ((2/n)+(2k/n^2))

6. lim as n->∞ ∑ from k=1 to n of ((5/n)+(k^3/n^4))

7. f(x)=3x+3; [0,3]

8. f(x)=x^2+5; [1,3]

RIEMANN SUM TABLES

1. ∫f(x) dx 0->10 where x=0, 2, 5, 7, 10 and f(x)=2, 3, 5, 7, 8

2. ∫f(x) dx 0->10 where x=0, 4, 6, 7, 10 and f(x)=5, 3, 2, 3, 5

3. ∫f(x) dx 0->14 where x=0, 3, 5, 9, 13, 14 and f(x)=-1, -2, -1, 0, -1, 0

4. ∫f(x) dx 0->19 where x=0, 4, 9, 10, 12, 19 and f(x)=-3, -5, -4, -2, -1, 1

FIRST FUNDAMENTAL THEOREM OF CALCULUS

1. ∫(-x^3+3x^2+1) dx from -1 to 3

2. ∫(x^4+x^3-4x^2+6) dx from -2 to 1

3. ∫(2x^2-12x+13) dx from 1 to 3

4. ∫(-x^3+3x^2-2) dx from 0 to 3

5. ∫(x^5-4x^3+4x+4) dx from -1 to 0

6. ∫4x^(1/3) dx from -3 to 0

7. ∫-(4/x^3) dx from -4 to -1

8. ∫4/x dx from -3 to -1

9. ∫2cos(x) dx from (-π/4) to (-π/6)

10. ∫1/(x√(x^2-1) dx from √2 to 2

11. ∫5(2x+4)^(1/3) dx from -3 to -2

12. ∫2/(2x+4)^3 dx from -1 to 2

13. ∫e^(2x-2) dx from -1 to 1

14. ∫(-x+|-3x-9|) dx from -4 to -2

15. ∫f(x) dx from 0 to 3 where f(x)={x/2-1 when x≤2, x^2-6x+8 when x>2

16. ∫-|x^2+4x| dx from -5 to 1

SUBSTITUTION FOR DEFINITE INTEGRALS

1. from -1 to 0 ∫8x/(4x^2+1)^2 dx; u=4x^2+1 

2. from 0 to 1 ∫-12x^2(4x^3-1)^3 dx; u=4x^3-1

3. from -1 to 2 ∫6x(x^2-1)^2 dx; u=x^2-1

4. from 0 to 1 ∫24x/(4x^2+4)^2 dx; u=4x^2+4

5. from -3 to 0 ∫-8x/(2x^2+3)^2 dx; u=2x^2+3

6. from 0 to 1 ∫16x/(4x^2+4)^2 dx; u=4x^2+4

7. from -1 to 0 ∫18x^2(3x^3+3)^2 dx; u=3x^3+3

8. from 0 to 1 ∫-8x/(4x^2+2)^2 dx; u=4x^2+2

MEAN VALUE THEOREM FOR INTEGRALS

1. f(x)=-x^2-2x+5; [-4,0]

2. f(x)=-x^4+2x^2+4; [-2,1]

3. f(x)=-x^2/2+x+3/2; [-3,1]

4. f(x)=4/x^2; [-4,-2]

5. f(x)=-x^3+7x^2-11x+3; [1,5]

6. f(x)=-x^5+3x^3; [0,1]

7. f(x)=4x^(1/2); [0,3]

8. f(x)=x^5-2x^3+x; [-1,0]

9. f(x)=1/x; [2,3]

10. f(x)=x^5-4x^3+2x-1; [-2,2]

11. f(x)=-x^5+4x^3-5x-3; [-2,0]

12. f(x)=x^5-2x^3-2; [-1,1]

13. f(x)=-x+2; [-2,2]

14. f(x)=-x^2-8x-17; [-6,-3]

15. f(x)=-3(2x-6)^(1/2); [3,5]

16. f(x)=4/(2x+6)^2; [-6,-5]

SECOND FUNDAMENTAL THEOREM OF CALCULUS

1. F(x)=∫ from -4 to x of (t-1) dt

2. F(x)=∫ from -3 to x of (t^2+2t+3) dt

3. F(x)=∫ from -1 to x^2 of (-2t+2) dt

4. F(x)=∫ from 4 to 3x of (-t^3+11t^2-39t+44) dt

5. F(x)=∫ from 2 to x^2 of (1/t^3) dt

6. F(x)=∫ from x to x^2 of (-2t-2) dt

7. F(x)=∫ from x to x^2 of (t^2-8t+11) dt

8. F(x)=∫ from x to 2x of (2/t) dt