Evaluate the definite integral: \(∫_0^\frac{π}{4} tanxdx\)
Solution and Explanation
Let I= \(∫_0^\frac{π}{4} tanxdx\)
\(∫tanxdx=-log|cosx|=F(x)\)
By second fundamental theorem of calculus,we obtain
\(I=F(\frac{π}{4})-F(0)\)
\(=-log|cos\frac{π}{4}|+log|cos0|\)
\(=-log|\frac{1}{√2}|+log|1|\)
\(=-log(2)\frac{1}{2}\)
\(=\frac{1}{2}log2\)
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Questions Asked in CBSE CLASS XII exam
Standard electrode potential for \( \text{Sn}^{4+}/\text{Sn}^{2+} \) couple is +0.15 V and that for the \( \text{Cr}^{3+}/\text{Cr} \) couple is -0.74 V. The two couples in their standard states are connected to make a cell. The cell potential will be:
To calculate the cell potential (\( E^\circ_{\text{cell}} \)), we use the standard electrode potentials of the given redox couples.
Given data:
\( E^\circ_{\text{Sn}^{4+}/\text{Sn}^{2+}} = +0.15V \)
\( E^\circ_{\text{Cr}^{3+}/\text{Cr}} = -0.74V \)- CBSE CLASS XII - 2025
- Electrochemistry
- “You speak peculiar things.” Why does Derry find Mr. Lamb’s conversation peculiar? (On the Face of It)
मोबाइल फोन विहीन दुनिया — 120 शब्दों में रचनात्मक लेख लिखिए :
- CBSE CLASS XII - 2025
- प्रश्न उत्तर
- Emily, Flora and Ginni entered into a partnership on 1st October, 2023 with capitals of ₹ 10,00,000 each. The partnership deed provided for interest on capital at 10% p.a. The firm earned a net profit of ₹ 7,50,000 for the year ended 31st March, 2024. The amount of profit transferred to Emily’s capital account was :
- CBSE CLASS XII - 2025
- Partnership Accounts
- "The Government had launched Incredible India Campaign to promote tourism in various parts of the country."
Elaborate the impact of Incredible India Campaign on foreign exchange reserves and Balance of Payment of India.- CBSE CLASS XII - 2025
- Balance of payments (BOP)
Concepts Used:
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus is the theorem which states that differentiation and integration are opposite processes (or operations) of one another.
Calculus's fundamental theorem connects the notions of differentiating and integrating functions. The first portion of the theorem - the first fundamental theorem of calculus – asserts that by integrating f with a variable bound of integration, one of the antiderivatives (also known as an indefinite integral) of a function f, say F, can be derived. This implies the occurrence of antiderivatives for continuous functions.