MTH1010_10_03_4

Question

MTH1010_10_03_4

BlackTom AI · Accepted Answer

First, consider the general rule: to find the antiderivative, we integrate each term separately and add a constant C at the end.

Option a): x^4 - cos(x) + C
- Integrate 4x^3: ∫4x^3 dx = x^4, since the power rule gives (4/4)x^4 = x^4.
- Integrate sin(x): ∫sin(x) dx = -cos(x).
- Combine: x^4 + (-cos(x)) + C = x^4 - cos(x) + C. This matches the expected result.

Option b): x^4 + cos(x) + C
- Here, sin(x) was incorrectly integrated as +cos(x) instead of -cos(x).
- The correct integral of sin(x) is negative cosine, so this option has the wrong sign for the trigonometric part.

Option c): (4/3) x^4 - cos(x) + C
- The term from integrating 4x^3 is not (4/3)x^4; it is x^4. This option uses an incorrect coefficient, which miscalculates the polynomial part.
- The sin part is correctly integrated as -cos(x), but the x^4 coefficient is wrong.

Option d): (4/3) x^4 + cos(x) + C
- This combines two errors: the coefficient (4/3) is incorrect for the x^4 term, and the sin(x) part has the wrong sign (cos(x) instead of -cos(x)).

Summary: The correct antiderivative is the one that yields x^4 - cos(x) + C, arising from ∫4x^3 dx = x^4 and ∫sin(x) dx = -cos(x). All other options mix up the coefficient or the sign of the cosine term.

MCD2130 - T2 - 2025 11.7 Online Quiz - MCD2130_QUIZ_TEN Differentiation and Integration

MTH1010_10_03_4

View Explanation

Log in for full answers

Similar Questions

Which answer is the correct anti-derivative (integral) for 3 𝑥 − 3 𝑥 − 4

Question at position 8 If y' = 6x - 3 and y(2) = 4, then y =6x2 - 3x + 2.3x2 - 3x + 2.3x2 - 3x.3x2 - 3x - 2.6.

Question at position 8 If y' = 6x - 3 and y(2) = 4, then y =6x2 - 3x + 2.3x2 - 3x - 2.6.3x2 - 3x + 2.3x2 - 3x.

Question text Find [math: ∫2x4+3x3−3x+4]\displaystyle\int{2\,x^4+3\,x^3-3\,x+4} [math: dx]. Note: Type "[math: c]" for the integral constant. [input] Check Question 15

MTH1010_10_08_3

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler