The Definite Integral

The lower estimate is:

(a)  

Answer explanation

Use left hand rectangles

The upper estimate is:

(a)  

Answer explanation

Use right hand rectangles

Estimate using a trapezoidal sum

(a)  

Answer explanation

Average the left and right hand rectangles

• $\int_1^5\frac{e^x}{1+x}dx$

• $\int_{ }^{ }\frac{e^x}{1+x}dx$

• $\int_1^5\left(\frac{e^x}{1+x}\right)\left(x\right)$

• 

Tags

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

• $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left(2+\frac{8i}{n}\right)^6\left(\frac{8}{n}\right)$

• $\sum_{i=1}^n\left(2+\frac{8i}{n}\right)^6\left(\frac{8}{n}\right)$

• $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left(\frac{8i}{n}\right)^6\left(\frac{8}{n}\right)$

• $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left(i\right)^6\left(\Delta x\right)$

Tags

CCSS.HSA.APR.A.1

• 3

• -3

• -6

• 0

(a)  

• $2\pi$

• $4\pi$

• $-2\pi$

• 4

Tags

CCSS.HSG.GMD.A.1

• $\frac{9}{2}-2\pi$

• $9-4\pi$

• $4.5+2\pi$

• 13

• 

(a)