Question

The approximate value of $\int₁⁵x²dx$ using trapezoidal rule with $n=4$ is

• A. 41
• B. 41.5
• C. 41.75
• D. 42

Hint:

The approximate value of $\int1xdx$ using trapezoidal rule with $n=4$ is

Answer 1

The Correct Option is D

Step 1: Concept
The trapezoidal rule formula is $\frac{h}{2} [f(x_0) + 2(f(x_1) + ... + f(x_{n-1})) + f(x_n)]$.
Step 2: Analysis
Here, $a=1, b=5, n=4$. Step size $h = (5-1)/4 = 1$. The x-values are 1, 2, 3, 4, 5.
Step 3: Evaluation
Using $f(x) = x^2$: $f(1)=1, f(2)=4, f(3)=9, f(4)=16, f(5)=25$.
Step 4: Conclusion
Value $= \frac{1}{2} [1 + 2(4+9+16) + 25] = \frac{1}{2} [1 + 58 + 25] = 42$.
Final Answer: (d)