SATHEE: Indefinite Integration 1 Question 62

Indefinite Integration 1 Question 62

63. The integral $\int_{0}^{1.5} [x^{2}] d x$ , where [.] denotes the greatest function, equals

$(1988, 2 M)$

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Solution:

$\int_{0}^{1.5} [x^{2}] d x = \int_{0}^{1} 0 d x + \int_{1}^{\sqrt{2}} 1 d x + \int_{\sqrt{2}}^{1.5} 2 d x$

$\begin{aligned} = 0 + [x]_{1}^{\sqrt{2}} + 2 [x]_{\sqrt{2}}^{1.5} \\ = (\sqrt{2} - 1) + 2 (1.5 - \sqrt{2}) \\ = \sqrt{2} - 1 + 3 - 2 \sqrt{2} \\ = 2 - \sqrt{2} \end{aligned}$

Indefinite Integration 1 Question 62

63. The integral $\int_{0}^{1.5} [x^{2}] d x$ , where [.] denotes the greatest function, equals

Match the Columns

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

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Sample Mock Test

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NCERT Exercise Video Solution

Indefinite Integration 1 Question 62

63. The integral ∫01.5[x2]dx, where [.] denotes the greatest function, equals

Match the Columns

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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63. The integral $\int_{0}^{1.5} [x^{2}] d x$ , where [.] denotes the greatest function, equals