Find the integral of x(4x² + 1) from 0 to 2. a. 18 c. 22 b. 16 d. 20

Question

Find the integral of x(4x² + 1) from 0 to 2. a. 18 c. 22 b. 16 d. 20

in progress 0
niczorrrr 4 years 2021-07-24T00:48:18+00:00 1 Answers 11 views 0

Answers ( )

  1. huyenthanh
    0
    2021-07-24T00:49:26+00:00
    Reply

    Answer:

    a. 18

    General Formulas and Concepts:

    Pre-Algebra

    Order of Operations: BPEMDAS

    1. Brackets
    2. Parenthesis
    3. Exponents
    4. Multiplication
    5. Division
    6. Addition
    7. Subtraction
    • Left to Right

    Distributive Property

    Algebra I

    • Terms/Coefficients

    Calculus

    Integrals

    • Definite Integrals

    Integration Rule [Reverse Power Rule]:                                                                      \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

    Integration Rule [Fundamental Theorem of Calculus 1]:                                        \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

    Integration Property [Multiplied Constant]:                                                             \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

    Integration Property [Addition/Subtraction]:                                                           \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

    Step-by-step explanation:

    Step 1: Define

    Identify

    \displaystyle \int\limits^2_0 {x(4x^2 + 1)} \, dx

    Step 2: Integrate

    1. [Integrand] Distribute x [Distributive Property]:                                              \displaystyle \int\limits^2_0 {(4x^3 + x)} \, dx
    2. Rewrite Integral [Integration Property – Addition/Subtraction]:                     \displaystyle \int\limits^2_0 {4x^3} \, dx + \int\limits^2_0 {x} \, dx
    3. Rewrite 1st Integral [Integration Property – Multiplied Constant]:                 \displaystyle 4\int\limits^2_0 {x^3} \, dx + \int\limits^2_0 {x} \, dx
    4. [Integrals] Reverse Power Rule:                                                                      \displaystyle 4(\frac{x^4}{4}) \bigg| \limits^2_0 + (\frac{x^2}{2}) \bigg| \limits^2_0
    5. Evaluate [Integration Rule – Fundamental Theorem of Calculus 1]:              \displaystyle 4(4) + 2
    6. Evaluate:                                                                                                           \displaystyle 18

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

    Unit: Integration

    Book: College Calculus 10e

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )