Which of the following integrals represents the area of the region bounded by x = 0, x = 1 and the functions f(x) = -2x4 and g(x) = x2?
the integral from 0 to 1 of the quantity, x squared plus 2 times x to the 4th power, dx
the integral from 0 to 1 of the quantity, x squared minus 2 times x to the 4th power, dx
the integral from 0 to 1 of the quantity, negative 2 times x to the 4th power minus x squared, dx
the integral from 0 to 1 of the quantity, x to the 4th power minus 4 times x to the 8th power, dx

A.  

General Formulas and Concepts:

Algebra I

Functions

Calculus

Integration

Area of a Region Formula:                                                                                    

Step-by-step explanation:

Step 1: Define

Identify

f(x) = -2x⁴

g(x) = x²

Interval bound [0, 1]

Step 2: Visualize

Graph the given and identify more information. See attachment.

Top function: g(x)

Bottom function: f(x)

Bounds of Integration: [0, 1]

Step 3: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

the answer is d

step-by-step explanation: