Integration Intergral Calculus and Definite Integral Problems

Please, use Desmos to graph the functions and shade the region. Type all your answers (includes equations) with detail on desmos.com for this assignment.

You will need to submit the following items for the two problems.

• Input your function and find the area under the line/curve.
• Graph your function and shade the region under or above the function bounded by x-axis.
• Print out answers and graph from desmos.com when submit your assignment.

Type your name with the date of completion on your Desmos file. 

INTERGRAL CALCULUS 

INTEGRATION, AREA UNDER A CURVE

DEFINITE INTEGRAL        

I.  For this problem, you will need to make up your own functions. Make sure to print out your graph from desmos.com and write down your calculations on desmos.com.

• a) Use desmos.com to input a linear function f(x)=mx+b and graph and shade the region between your function and x-axis. 
• a) Use desmos.com to input a piece-wise function  of g(x) with two linear functions with domain value of -5 to 5, graph and shade the region between your functions and x-axis. Set up a definite integral and find the area under g(x) with domain value of -5 to 5. 
• a) Use desmos.com to input a polynomial function degree of 2 or higher h(x) with domain value of -3 to 3, graph and shade the region you are trying to determine. Set up a definite integral and find the area under h(x) with domain value of -3 to 3. 

Set up a definite integral and find the area under f(x) with domain value say from – 4 to 4.  

b) Use Geometry to solve for the same function from part (a). 

Compare your results and comment. Do you find the area under the line the same as part (a)?