State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_"a"^"b" f("t")*dt`

`int_"a"^"b" f(x)*dx = int_"a"^"b" f("t")*dt` True.

State whether the following is True or False : ∫abf(x)⋅dx=∫abf(t)⋅dt - Mathematics and Statistics

प्रश्न

State whether the following is True or False : $\int_{a}^{b} f (x) \cdot d x = \int_{a}^{b} f (t) \cdot d t$

विकल्प

True
False

MCQ

सत्य या असत्य

उत्तर

$\int_{a}^{b} f (x) \cdot d x = \int_{a}^{b} f (t) \cdot d t$ True.

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Fundamental Theorem of Integral Calculus

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q III) 2)Q III) 1)Q III) 3)

अध्याय 6: Definite Integration - MISCELLANEOUS EXERCISE - 6 [पृष्ठ १४९]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board

अध्याय 6 Definite Integration
MISCELLANEOUS EXERCISE - 6 | Q III) 2) | पृष्ठ १४९

संबंधित प्रश्न

Prove that:

$\begin{array}{l} \int_{- a}^{a} f (x) d x = 2 \int_{0}^{a} f (x) d x, & If f (x) is an even function \\ = 0, & if f (x) is an odd function \end{array}$

Evaluate : $\int_{0}^{\frac{π}{4}} \frac{\cos x}{4 - \sin^{2} x} \cdot d x$

Evaluate:

$\int_{0}^{1} \sqrt{\frac{1 - x}{1 + x}} \cdot d x$

Evaluate : $\int_{0}^{\frac{π}{2}} \frac{\sin x - \cos x}{1 + \sin x \cos x} \cdot d x$

Choose the correct option from the given alternatives :

If $\frac{d x}{\sqrt{1 + x} - \sqrt{x}} = \frac{k}{3}$ , then k is equal to

Evaluate the following : $\int_{0}^{1} (\cos^{- 1} x^{2}) \cdot d x$

Evaluate the following : $\int_{1}^{\infty} \frac{1}{\sqrt{x} (1 + x)} \cdot d x$

Evaluate the following : $\int_{0}^{\frac{π}{2}} [2 \log (\sin x) - \log (\sin 2 x)] \cdot d x$

Choose the correct alternative :

$\int_{2}^{3} x^{4} \cdot d x$ =

Fill in the blank : $\int_{2}^{3} x^{4} \cdot d x$ = _______

State whether the following is True or False : $\int_{0}^{a} f (x) \cdot d x = \int_{a}^{0} f (a - x) \cdot d x$

Solve the following:

$\int_{0}^{1} e^{x^{2}} \cdot x^{3} d x$

Solve the following : $\int_{0}^{1} \frac{1}{\sqrt{1 + x} + \sqrt{x}} d x$

$\int_{1}^{2} \frac{e^{\frac{1}{x}}}{x^{2}} d x$ =

$\int_{0}^{a} 4 x^{3} d x$ = 81, then a = ______

State whether the following statement is True or False:

$\int_{0}^{a} 3 x^{2} d x$ = 27, then a = 2.5

Evaluate $\int_{0}^{a} x^{2} {(a - x)}^{\frac{3}{2}} d x$

Evaluate the following integral:

$\int_{0}^{1} x {(1 - x)}^{5} d x$

Evaluate the following definite integral:

$\int_{4}^{9} \frac{1}{\sqrt{x}} d x$

Evaluate the following definite intergral:

$\int_{- 2}^{3} \frac{1}{x + 5} d x$

State whether the following is True or False : ∫abf(x)⋅dx=∫abf(t)⋅dt - Mathematics and Statistics

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State whether the following is True or False : ∫abf(x)⋅dx=∫abf(t)⋅dt - Mathematics and Statistics

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