Project ForgeEngineering Mathematics
Numerical Methods
GATE 2009
Medium
Using the trapezoidal rule and 4 equal intervals (n=4), the calculated value of the integral ∫₀^π sin(θ)dθ (rounded to the first place of decimal) is
- A1.7
- 1.9
- C2.0
- D2.1
Explanation
h=π/4. Values: sin(0)=0, sin(π/4)=0.7071, sin(π/2)=1, sin(3π/4)=0.7071, sin(π)=0. Trapezoidal sum=(h/2)[f0+2f1+2f2+2f3+f4]=(π/8)[0+1.4142+2+1.4142+0]=(0.3927)(4.8284)≈1.90.
Source: GATE CH 2009 (2009)
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