Integration Lesson AB Calculus

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{1}{n}$$  

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3i}{n}$$  

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$$  

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$$  

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\frac{i}{n}$$  

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\frac{i}{n}$$  

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\frac{\pi}{n}$$  

$$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\frac{\pi}{n}$$  

$$\int_0^5\left(x^2+x+1\right)dx$$  

$$\int_5^6\left(x^2+x+1\right)dx$$  

$$\int_0^1\left(\left(5x\right)^2+5x+1\right)dx$$  

$$\int_0^{10}\left(\frac{x^2}{2}+\frac{x}{2}+1\right)dx$$  

$$\int_3^7\left(2+\sqrt{x}\right)dx$$  

$$\int_0^4\left(2+\sqrt{x}\right)dx$$  

$$\int_3^7\left(2x+\sqrt{x}\right)dx$$  

$$\int_3^7\left(2+\sqrt{3+x}\right)dx$$  

-1

7

2

9

$$-\int_3^7h\left(\alpha\right)d\alpha$$  

$$-\int_7^9h\left(\alpha\right)d\alpha$$  

$$\int_7^9h\left(\alpha\right)d\alpha$$  

None of the following are equivalent to the given

0

7 + c

7x + c

-7x + c

$$x^3+4x^2+c$$  

$$x^3+2x^2+c$$  

$$\frac{3}{2}x^3+4x^2+c$$  

$$3x^3+4x^2+c$$  

0

4t + C

4x + C

2x² + C

-18

4x - 9x²

4x - 9x² + C

(4 - 18x)² /2 + C

$$1+c$$  

$$\ln\ \left|x\right|\ +c$$  

$$-\frac{1}{x^2}+c$$  

$$x^0+c$$  

sin(x)+c

-sin(x)+c

-cos(x)+c

$$\cos^2\left(x\right)+c$$

cos(x)+c

-cos(x)+c

-sin(x)cos(x)+c

$$\sin^2\left(x\right)+c$$

tan(x)+c

sec(x)+c

csc(x)+c

-csc(x)+c

sec(x)+c

tan(x)+c

2sec(x)+c

-csc(x)+c

$$ex$$

$$e^x$$

$$e^x+c$$

$$\ln\left(x\right)+c$$

$$\sqrt[]{x+c}$$

$$\sqrt[]{x}+c$$

$$\left(\sqrt[]{x}\right)^2+c$$

$$\left(\sqrt[]{x}\right)^{\frac{1}{2}}+c$$

An unknown constant

The axis of symmetry

The coefficient

A trig value

Indefinite Integral

Definite Integral

Integration

Differentiation

Integration

Differentiation

Limitation

continuation