#integral

Integral Calculus 2

Find the area of region bounded by the curve y² = x and the line x = 1, x = 4 and the x-axis

In easy words, we verify 14/3 by full calculation: use standard identity, substitute, simplify step by step to reach 14/3.

Ref: NCERT Mathematics Class XII — Integrals

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Integral Calculus 2

If _0^/2sinx/sinx + cosxdx = g''(x) + C where g'(1) = 1 then C will be

The trick is we verify C = /4 - 1 by full calculation: use standard identity, substitute, simplify step by step to reach C = /4 - 1.

Ref: NCERT Mathematics Class XII — Integrals

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Integral Calculus 2

If f(x) and g(x) are continuous functions satisfying f(x) = f(a – x) and g(x) + g(a – x) = 2, then what is _0^a f( x )g(

Applying the basic concept, complete solution: write formula, plug data, do arithmetic. Final value matches _0^a f( x )dx. Simple and accurate.

Ref: NCERT Mathematics Class XII — Integrals

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Integral Calculus 2

The differentiation of Integral I = _ x^ x t^2 dt with respect to x at x = π/4?

Simply put, we verify √2 log 2 by full calculation: use standard identity, substitute, simplify step by step to reach √2 log 2.

Ref: NCERT Mathematics Class XII — Integrals

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