KCET · Maths · Three Dimensional Geometry
\( 3.5 \)
\( \int_{0.2}[x] d x \) is equal to
- A \( 04 \)
- B \( 4.5 \)
- C \( 3 . .5 \)
- D \( 03 \)
Answer & Solution
Correct Answer
(B) \( 4.5 \)
Step-by-step Solution
Detailed explanation
Given that,
\(\int_{0.2}^{3.5}[x] d x\)
\(=\int_{0.2}^{1} 0 \cdot d x+\int_{1}^{2} 1 . d x+\int_{2}^{3} 2 . d x+\int_{3}^{3.5} 3 d x\)
\(=0+1[x]_{1}^{2}+2[x]_{2}^{3}+3[x]_{3}^{3.5}\)
\(=0+1(2-1)+2(3-2)+3(3.5-3)\)
\(=0+1+2+1.5=4.5\)
\(\int_{0.2}^{3.5}[x] d x\)
\(=\int_{0.2}^{1} 0 \cdot d x+\int_{1}^{2} 1 . d x+\int_{2}^{3} 2 . d x+\int_{3}^{3.5} 3 d x\)
\(=0+1[x]_{1}^{2}+2[x]_{2}^{3}+3[x]_{3}^{3.5}\)
\(=0+1(2-1)+2(3-2)+3(3.5-3)\)
\(=0+1+2+1.5=4.5\)
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